×

zbMATH — the first resource for mathematics

Lie superalgebras. (English. Russian original) Zbl 0567.17003
J. Sov. Math. 30, 2481-2512 (1985); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 25, 3-49 (1984).
This is a survey of results on the representation theory of “classical” Lie superalgebras. The author reviews 131 papers. In §1 (classical Lie superalgebras over \(\mathbb C)\) the matrix Lie superalgebras, Lie superalgebras of (formal) vector fields, exceptional Lie superalgebras, Lie superalgebras of string theories, Kac superalgebras \(g_{\phi}^{(m)}\) and Kac-Moody superalgebras are considered. The modules over Lie superalgebras of vector fields are studied in §2. In §3 it is established that every irreducible topological module over the Lie superalgebra \({\mathcal L}\) of vector fields is realized as a submodule in some topological \({\mathcal L}\)-module \(T(V)\) (here \(T(V)\) is the superspace of formal tensor fields of type \(V\) which are constructed by means of a finite-dimensional \(L_ 0\)-module \(V\)). The author’s purpose is the description of this submodule. The characters of irreducible modules are investigated in §4. Finally other results on Lie superalgebras are enumerated in §5.

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D. V. Alekseevskii, D. A. Leites, and I. M. Shchepochkina, ”Examples of simple, infinite-dimensional Lie superalgebras of vector fields,” Dokl. Bolg. Akad. Nauk,33, No. 9, 1187–1190 (1980). · Zbl 0457.17005
[2] A. A. Beilinson, ”Coherent sheaves on Pn and problems of linear algebra,” Funkts. Anal. Prilozhen.,12, No. 3, 68–69 (1978). · Zbl 0427.57013 · doi:10.1007/BF01077575
[3] A. A. Beilinson, ”The derived category of coherent sheaves on Pn,” in: Vopr. Teor. Grupp i Gomol. Algebry (Yaroslavl’), No. 2, 42–54 (1979).
[4] F. A. Berezin, ”Representations of the supergroup U(p, q),” Funkts. Anal. Prilozhen.,10, No. 3, 70–71 (1976). · Zbl 0337.22013
[5] F. A. Berezin, Introduction to Algebra and Analysis in Commuting and Anticommuting Variables [in Russian], Moscow State Univ. (1983). · Zbl 0527.15020
[6] F. A. Berezin and D. A. Leites, ”Supermanifolds,” Dokl. Akad. Nauk SSSR,224, No. 3, 505–508 (1975). · Zbl 0331.58005
[7] I. N. Bernshtein, I. M. Gel’fand, and S. I. Gel’fand, ”Algebraic bundles on Pn and problems of linear algebra,” Funkts. Anal. Prilozhen.,12, No. 3, 66–68 (1978).
[8] I. N. Bernshtein and D. A. Leites, ”Integral forms and the Stokes formula on supermanifolds,” Funkts. Anal. Prilozhen.,11, No. 1, 55–56 (1977). · Zbl 0368.35046 · doi:10.1007/BF01135536
[9] I. N. Bernshtein and D. A. Leites, ”Irreducible representations of finite-dimensional Lie superalgebras of the series W,” in: Vopr. Teorii Grupp i Gomol. Algebry (Yaroslavl’), No. 2, 187–193 (1979). · Zbl 0443.17003
[10] I. N. Bernshtein and D. A. Leites, ”A formula for the characters of irreducible finite-dimensional representations of Lie superalgebras of the series H and sl,” Dokl. Bolg. Akad. Nauk,33, No. 8, 1049–1051 (1980). · Zbl 0457.17002
[11] I. N. Bernshtein and D. A. Leites, ”Invariant differential operators and irreducible representations of a Lie algebra of vector fields,” Serdika B”lg. Mat. Spisanie,7, 320–334 (1981). · Zbl 0506.17003
[12] N. Bourbaki, Lie Groups and Algebras [Russian translation], Mir, Moscow (1978).
[13] Yu. I. Manin (ed.), Geometric Ideas in Physics [Russian translation], Mir, Moscow (1983).
[14] P. Ya. Grozman, ”Classification of bilinear invariant operators on tensor fields,” Funkts. Anal. Prilozhen.,14, No. 2, 58–59 (1980). · Zbl 0432.58025
[15] J. Dixmier, Enveloping Algebras, Elsevier (1977).
[16] V. G. Drinfel’d and Yu. I. Manin, ”Yang-Mills fields, instantons, tensor products of instantons,” Yad. Fiz.,29, No. 6, 1646–1654 (1979). · Zbl 0536.58010
[17] A. A. Zaitsev and L. V. Nikolenko, ”Indecomposable representations of the Grassman algebra,” Funkts. Anal. Prilozhen.,4, No. 3, 101–102 (1970).
[18] V. G. Kats, ”On the classification of simple Lie superalgebras,” Funkts. Anal. Prilozhen.,9, No. 3, 91–92 (1975).
[19] V. G. Kats, ”Classification of simple algebraic supergroups,” Usp. Mat. Nauk,32, No. 3, 214–215 (1977).
[20] V. G. Kats, ”Letter to the editor,” Funkts. Anal. Prilozhen.,10, No. 2, 93 (1976).
[21] A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1972).
[22] A. A. Kirillov, ”On invariant differential operators on geometric quantities,” Funkts. Anal. Prilozhen.,11, No. 2, 39–44 (1977).
[23] A. A. Kirillov, ”Invariant operators on geometric quantities,” in: Sovremennye Problemy Matematiki, Vol. 16 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1980), pp. 3–29.
[24] A. A. Kirillov, ”Orbits of the group of diffeomorphisms of the circle and local Lie superalgebras,” Funkts. Anal. Prilozhen.,15, No. 2, 75–76 (1981). · Zbl 0466.58012
[25] R. Yu. Kirillova, ”Explicit solutions of supered Toda lattices,” in: Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. AN SSSR,123 (1983), pp. 98–111.
[26] I. A. Kostrikin, ”Irreducible graded representations of Lie algebras of Cartan type,” Dokl. Akad. Nauk SSSR,243, No. 3, 565–567 (1978). · Zbl 0412.17013
[27] I. A. Kostrikin, ”Representations of height 1 of infinite-dimensional Lie algebras of the series K,” Moscow State Univ., No. 2737-79 Dep (1979).
[28] Yu. Yu. Kochetkov, ”Irreducible induced representations of Leites superalgebras,” in: Vopr. Teoriii Grupp i Gomol. Algebry (Yaroslavl’), No. 3, 120–123 (1983). · Zbl 0578.17004
[29] Yu. Yu. Kochetkov, ”Irreducible induced representations of Lie superalgebras of the series SLe(n),” YarGU, No. 3917-83 Dep (1983).
[30] A. N. Leznov and M. V. Savel’ev, Group Methods of Integrating Nonlinear Dynamical Systems [in Russian], Nauka, Moscow (1984).
[31] D. A. Leites, ”Cohomologies of Lie superalgebras,” Funkts. Anal. Prilozhen.,9, No. 4, 75–76 (1975). · Zbl 0336.20032 · doi:10.1007/BF01078190
[32] D. A. Leites, ”Introduction to the theory of supermanifolds,” Usp. Mat. Nauk,35, No. 1, 3–57 (1980). · Zbl 0439.58007
[33] D. A. Leites, ”A formula for the characters of irreducible, finite-dimensional representations of Lie superalgebras of the series C,” Dokl. Bolg. Akad. Nauk,33, No. 8, 1053–1055 (1980). · Zbl 0457.17003
[34] D. A. Leites, ”Formulas for the characters of irreducible, finite-dimensional representations of simple Lie superalgebras,” Funkts. Anal. Prilozhen.,14, No. 2, 35–39 (1980). · Zbl 0431.17005
[35] D. A. Leites, Irreducible representations of Lie superalgebras of vector fields and invariant differential operators,” Funkts. Anal. Prilozhen.,16, No. 1, 76–78 (1982). · Zbl 0493.58023
[36] D. A. Leites, ”Automorphisms and real forms of Lie superalgebras of vector fields,” in: Vopr. Teorii Grupp i Gomol. Algebry (Yaroslavl’) (1983), pp. 126–127. · Zbl 0578.17003
[37] D. A. Leites, ”Representations of Lie superalgebras,” Teor. Mat. Fiz.,52, No. 2, 225–228 (1982). · Zbl 0503.17002 · doi:10.1007/BF01018415
[38] D. A. Leites, ”Irreducible representations of Lie superalgebras of divergence-free vector fields and invariant differential operators,” Serkida B”lg. Mat. Spisanie,8, No. 1, 12–15 (1982). · Zbl 0529.17002
[39] D. A. Leites, Theory of Supermanifolds [in Russian], Izd. KFAN SSSR, Petrozavodsk (1983). · Zbl 0599.58001
[40] D. A. Leites, ”Clifford algebras as superalgebras and quantization,” Teor. Mat. Fiz.,58, No. 2, 229–232 (1984). · Zbl 0535.58029
[41] D. A. Leites and M. A. Semenov-Tyan-Shanskii, ”Lie superalgebras and integrable systems,” in: Zap. Nauchn. Seminarov Leningr. Otd. Mat. Inst. AN SSSR, Vol. 123, Nauka, Leningrad (1983), pp. 92–97. · Zbl 0526.58025
[42] D. A. Leites and V. V. Serganova, ”Solutions of the classical Yang-Baxter equation for simple Lie superalgebras,” Teor. Mat. Fiz.,58, No. 1, 26–37 (1984). · Zbl 0537.22014
[43] D. A. Leites and B. L. Feigin, ”Kac-Moody superalgebras,” in: Teoretiko-gruppovye Metody v Fizike [in Russian], Vol. 1, Nauka, Moscow (1983), pp. 274–278.
[44] D. A. Leites and B. L. Feigin, ”New Lie superalgebras of string theories,” in: Teoretiko-gruppovye Metody v Fizike [in Russian], Vol. 1, Nauka, Moscow, pp. 269–273.
[45] Yu. I. Manin, Gauge Fields and Complex Geometry [in Russian], Nauka, Moscow (1984), pp. 3–80.
[46] Yu. I. Manin, ”Holomorphic supergeometry and Yang-Mills superfields,” in: Sovremennye Problemy Matematiki, Vol. 24 (Itogi Nauki i Tekh. VINITI AN SSSR), Moscow (1984). · Zbl 0557.53051
[47] M. S. Marinov, ”Relativistic strings and dual models of strong interactions,” Usp. Fiz. Nauk,121, No. 3, 377–425 (1977). · doi:10.3367/UFNr.0121.197703a.0377
[48] M. V. Mosalova, ”On functions of noncommuting operators generating graded Lie algebras,” Mat. Zametki,29, No. 1, 35–44 (1980).
[49] V. I. Ogievetskii, ”Geometry of supergravitation,” in: Problemy Kvantovoi Teorii Polya, JINR, Dubna (1981), pp. 187–200.
[50] V. I. Ogievetskii and L. Mezinchesku, ”Symmetries between bosons and fermions and superfields,” Usp. Fiz. Nauk,117, No. 4, 637–683 (1975). · doi:10.3367/UFNr.0117.197512b.0637
[51] V. S. Retakh, ”Massa operations in Lie superalgebras and differentials of the Quillen spectral sequence,” Funkts. Anal. Prilozhen.,12, No. 4, 91–92 (1978).
[52] V. S. Retakh and B. L. Feigin, ”On cohomologies of some Lie algebras and superalgebras of vector fields,” Usp. Mat. Nauk,37, No. 2, 233–234 (1982). · Zbl 0493.58029
[53] A. N. Rudakov, ”Irreducible representations of infinite-dimensional Lie algebras of Cartan type,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 3, 835–866 (1974). · Zbl 0322.17004
[54] A. N. Rudakov, ”Irreducible representations of finite-dimensional Lie algebras of the series S and H,” Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 3, 496–511 (1975). · Zbl 0345.17008
[55] V. V. Serganova, ”Real forms of Kac-Moody superalgebras,” in: Teoretiko-gruppovye Metody v Fizike [in Russian], Vol. 1, Nauka, Moscow (1983), pp. 279–282.
[56] V. V. Serganova, ”Classification of simple real Lie superalgebras and symmetric superspaces,” Funkts. Anal. Prilozhen.,17, No. 3, 46–54 (1983). · Zbl 0545.17001
[57] V. V. Serganova, ”Automorphisms and real forms of the superalgebras of string theories,” Izv. Akad. Nauk SSSR, Ser. Mat.,48, No. 2 (1984). · Zbl 0545.17002
[58] A. N. Sergeev, ”Invariant polynomial functions on Lie superalgebras,” Dokl. Bolg. Akad. Nauk,35, No. 5, 573–576 (1982). · Zbl 0501.17003
[59] A. A. Slavnov, ”Supersymmetric gauge theories and their possible applications to weak and electromagnetic interactions,” Usp. Fiz. Nauk,124, No. 3, 487–508 (1978). · doi:10.3367/UFNr.0124.197803e.0487
[60] Group-Theoretic Methods in Physics [in Russian], Vols. 1, 2, Nauka, Moscow (1983).
[61] B. L. Feigin and D. B. Fuks, ”Verma modules over a Virasoro algebra,” Funkts. Anal. Prilozhen.,17, No. 3, 91–92 (1982). · Zbl 0526.17010
[62] D. Fridman and P. van N’yuvenkheizen, ”Supergravitation and unification of the laws of physics,” Usp. Fiz. Nauk,128, No. 1, 135–156 (1979). · doi:10.3367/UFNr.0128.197905e.0135
[63] D. B. Fuks, Cohomologies of Infinite-Dimensional Lie Algebras [in Russian], Nauka, Moscow (1984). · Zbl 0592.17011
[64] Kh’eu NguenVan, ”On the theory of representations of the superalgebra of extended supersymmetry,” Ob”edin. Inst. Yad. Issled., Dubna, Soobshch., No. P2-82-819 (1982).
[65] A. V. Shapovalov, ”Real irreducible representations of Hamiltonian Lie superalgebras,” No. 3448-80 Dep, Moscow State Univ. (1980).
[66] A. V. Shapovalov, ”Finite-dimensional irreducible representations of Hamiltonian Lie superalgebras,” Mat. Sb.,107, No. 2, 259–274 (1978). · Zbl 0401.17008
[67] A. V. Shapovalov, ”Invariant differential operators and irreducible representations of finite-dimensional Hamiltonian and Poisson Lie superalgebras,” Serdika B”lg. Mat. Spisanie,7, No. 4, 337–342 (1981). · Zbl 0502.58016
[68] G. S. Shmelev, ”Differential operators invariant relative to the Lie superalgebra H (2| 2; \(\lambda\)) and its irreducible representations,” Dokl. Bolg. Akad. Nauk,35, No. 3, 287–290 (1982). · Zbl 0493.58024
[69] G. S. Shmelev, ”Invariant operators in symplectic superspace,” Mat. Sb.,112, No. 4, 21–38 (1983).
[70] G. S. Shmelev, ”Irreducible representations of infinite-dimensional Hamiltonian and Poisson Lie superalgebras and invariant differential operators,” Serdika B”lg. Mat. Spisanie,8, No. 4, 408–417 (1982). · Zbl 0532.17009
[71] G. S. Shmelev, ”Irreducible representations of Poisson Lie superalgebras and invariant differential operators,” Funkts. Anal. Prilozhen.,17, No. 1, 91–92 (1983). · Zbl 0541.58024
[72] G. S. Shmelev, ”Classification of indecomposable finite-dimensional representations of the Lie superalgebra W(0, 2),” Dokl. Bolg. Akad. Nauk,35, No. 8, 1025–1027 (1982). · Zbl 0511.17001
[73] I. M. Shchepochkina, ”Exceptional simple infinite-dimensional Lie superalgebras,” Dokl. Bolg. Akad. Nauk,36, No. 3, 313–314 (1983). · Zbl 0559.17003
[74] Ademollo et al., ”Dual string models, part 1,” Nucl. Phys.,B111, 1, 77–100 (1976); Part 2, Nucl. Phys.,B114, 2, 297–316 (1976). · doi:10.1016/0550-3213(76)90483-1
[75] Ademollo et al., ”Supersymmetric strings and colour confinement,” Phys. Lett.,B62, 1, 105–110 (1976). · doi:10.1016/0370-2693(76)90061-7
[76] A. B. Balantekin and I. Bars, ”Dimension and character formulas for Lie supergroups,” J. Math. Phys.,22, No. 6, 1149–1162 (1981). · Zbl 0469.22017 · doi:10.1063/1.525038
[77] A. B. Balantekin, ”Representations of supergroups,” J. Math. Phys.,22, No. 8, 1810–1818 (1981). · Zbl 0547.22014 · doi:10.1063/1.525127
[78] A. B. Balantekin and I. Bars, ”Branching rules for the supergroups SU(N/M) from those of SU(N+M),” J. Math. Phys.,23, No. 7, 1239–1247 (1982). · Zbl 0488.22040 · doi:10.1063/1.525508
[79] I. Bars, B. Morel, and H. Ruegg, ”Kac-Dynkin diagrams and supertableaux,” J. Math. Phys.,24, No. 4, 201D–2262 (1983). · Zbl 0547.22015 · doi:10.1063/1.525970
[80] A. Beillinson and J. Bernstein, ”Localisation de of modules,” C. R. Acad. Sci., Paris,292, No. 1, I-15–I-18 (1981). · Zbl 0476.14019
[81] A. Berele and A. Regev, ”Hooke-Young diagrams, combinatorics, and representations of Lie superalgebras,” Bull. (New Series) Am. Math. Soc.,8, No. 2, 337–339 (1983). · Zbl 0506.17002 · doi:10.1090/S0273-0979-1983-15110-8
[82] F. A. Berezin, ”The construction of Lie supergroups U(p, q) and C(m, n),” ITEP-76, Moscow, ITEP (1977).
[83] F. A. Berezin, ”The radial parts of the Laplace operators on the Lie supergroups U(p, q) and C(m, n),” ITEP-75, Moscow, ITEP (1977).
[84] F. A. Berezin, ”Lie superalgebras,” ITEP-66, Moscow, ITEP (1977).
[85] F. A. Berezin, ”The Laplace-Casimir operators (general theory),” ITEP (1977).
[86] F. A. Berezin and V. N. Tolstoy, ”The group with Grassman structure VOSp(1, 2),” Commun. Math. Phys.,78, No. 3, 409–428 (1981). · Zbl 0452.22020 · doi:10.1007/BF01942332
[87] J. N. Bernstein and D. A. Leites, ”The superalgebra Q(n), the odd trace, and the odd determinant,” Dokl. Bolg. Akad. Nauk,35, No. 3, 285–286 (1982). · Zbl 0494.17002
[88] J. Blank et al., ”Boson-fermion representations of Lie superalgebras. The example of osp(1, 2),” J. Math. Phys.,23, No. 3, 350–353 (1982). · Zbl 0635.17010 · doi:10.1063/1.525373
[89] R. Blok, ”Classification of the irreducible representations of S1(2, C),” Bull. Am. Math. Soc. (New Series),1, No. 1, 247–250 (1979). · Zbl 0412.17009 · doi:10.1090/S0273-0979-1979-14573-7
[90] J. L. Brylinski and M. Kashiwara, ”Kazhdan-Lusztig conjecture and holonomic systems,” Invent. Math.,64, 387 (1981). · Zbl 0473.22009 · doi:10.1007/BF01389272
[91] L. Corwin, Y. Ne’eman, and S. Sternberg, ”Lie algebras in mathematics and physics,” Rev. Mod. Phys.,47, 573–604 (1975). · Zbl 0557.17004 · doi:10.1103/RevModPhys.47.573
[92] D. Z. Djokovic, ”Superlinear algebras or two-graded algebraic structures,” Can. J. Math.,30, No. 6, 1336–1344 (1978). · Zbl 0405.15023 · doi:10.4153/CJM-1978-111-5
[93] V. V. Deodhar, O. Gabber, and V. G. Kac, ”Structure of some categories of representations of infinite-dimensional Lie algebras,” Adv. Math.,45, 92–116 (1982). · Zbl 0491.17008 · doi:10.1016/S0001-8708(82)80014-5
[94] I. B. Frenkel, ”Spinor representation of affine Lie algebras,” Proc. Nat. Acad. Sci. USA Phys. Sci.,77, No. 11, 6303–6306 (1980). · Zbl 0451.17004 · doi:10.1073/pnas.77.11.6303
[95] I. B. Frenkel and V. G. Kac, ”Basic representations of affine Lie algebras and dual resonance models, Invent. Math.,62, No. 1, 23–30 (1980). · Zbl 0493.17010 · doi:10.1007/BF01391662
[96] F. Cursey and L. Marchildon, ”The graded Lie groups SU(2, 2/1) and OSp(1/4),” J. Math. Phys.,19, No. 5, 942–951 (1978). · Zbl 0389.22020 · doi:10.1063/1.523797
[97] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York (1978). · Zbl 0451.53038
[98] L. Hlavaty and J. Niederle, ”Casimir operators of the simplest supersymmetry superalgebras,” Lett. Math. Phys.,4, No. 4, 301–306 (1980). · Zbl 0445.17003 · doi:10.1007/BF00402579
[99] J. W. B. Hughes, ”SU(2) shift operators and representations of Spl(2, 1),” Group Theor. Math. Phys., Kiryat Anavim, 1979, Bristol, e.a., pp. 320–322.
[100] J. W. B. Hughes, ”Representations of osp (2, 1) and the metaplectic representations,” J. Math. Phys., No. 2, 245–250 (1981). · Zbl 0456.22013 · doi:10.1063/1.524895
[101] J. P. Hurni and B. Morel, ”Irreducible representations of the superalgebras of type II,” J. Math. Phys.,23, No. 12, 2236–2243 (1982). · Zbl 0501.17002 · doi:10.1063/1.525314
[102] J. P. Hurni and B. Morel, ”Irreducible representations of SU(m/n),” J. Math. Phys.,24, No. 1, 157–163 (1983). · Zbl 0557.17002 · doi:10.1063/1.525573
[103] V. G. Kac, ”A sketch of Lie superalgebras theory,” Commun. Math. Phys.,53, No. 1, 31–64 (1977). · Zbl 0359.17009 · doi:10.1007/BF01609166
[104] V. G. Kac, ”Lie superalgebras,” Adv. Math.,26, 8–96 (1977). · Zbl 0366.17012 · doi:10.1016/0001-8708(77)90017-2
[105] V. G. Kac, ”Infinite-dimensional algebras, Dedekind’s \(\eta\)-function, classical Moebius function, and the very strange formula,” Adv. Math.30, 85–136 (1978). · Zbl 0391.17010 · doi:10.1016/0001-8708(78)90033-6
[106] V. G. Kac, ”Representations of classical Lie superalgebras,” Lect. Notes Math.,676, 597–626 (1978). · Zbl 0388.17002 · doi:10.1007/BFb0063691
[107] V. G. Kac, ”On simplicity of certain infinite-dimensional Lie algebras,” Bull. Am. Math. Soc,2, No. 2, 311–314 (1980). · Zbl 0427.17012 · doi:10.1090/S0273-0979-1980-14746-1
[108] V. G. Kac, ”An euclidation of ’Infinite-dimensional algebras ... and the very strange formula,’ E8 (1) and the cube root of the modular invariant theory,” Adv. Math.,35, 264–273 (1980). · Zbl 0431.17009 · doi:10.1016/0001-8708(80)90052-3
[109] V. G. Kac, ”Some problems on infinite-dimensional Lie algebras and their representations,” Lect. Notes Math.,933, 117–126 (1983). · doi:10.1007/BFb0093356
[110] V. G. Kac, Infinite-Dimensional Lie Algebras. An Introduction, Birkhauser, New York (1983). · Zbl 0537.17001
[111] V. G. Kac, ”Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras,” Commun. Alg.,5, 1375–1400 (1977). · Zbl 0367.17007 · doi:10.1080/00927877708822224
[112] I. Kaplansky, ”Superalgebras,” Pac. J. Math.,86, No. 1, 93–98 (1980). · Zbl 0438.17003 · doi:10.2140/pjm.1980.86.93
[113] I. Kaplansky, ”Some simple Lie algebras of characteristic 2,” Lect. Notes Math.,933, 127–129 (1982). · Zbl 0493.17005 · doi:10.1007/BFb0093357
[114] J. L. Koszul, ”Les algebras de Lie gradues de type sl(n, 1) et l’operateur de A. Capelli,” C. R. Acad. Sci.,292, Ser. 1, No. 2, 139–141 (1981).
[115] F. W. Lemiere and J. Patera, ”Congruence classes of finite-dimensional representations of simple Lie superalgebras,” J. Math. Phys.,23, No. 8, 1409–1414 (1982). · Zbl 0502.17005 · doi:10.1063/1.525531
[116] J. Lukierski, ”Graded orthosymplectic geometry and invariant fermionic \(\sigma\)-models,” Lett. Math. Phys.,3, No. 2, 135–140 (1979). · doi:10.1007/BF00400068
[117] J. Lukierski, ”Complex and quaternionic supergeometry,” Supergravity Proc. Workshop, Stony Brook (1975), Amsterdam e.a. (1979), pp. 85–92.
[118] J. Lukierski, ”Quaternionic and supersymmetric \(\sigma\)-models,” Lect. Notes Math.,836, 221–245 (1980). · Zbl 0456.53040 · doi:10.1007/BFb0089738
[119] M. Marcu, ”The tensor product of two irreducible representations of the Spl(2, 1) superalgebra,” J. Math. Phys.,21, No. 6, 1284–1292 (1980). · Zbl 0445.17004 · doi:10.1063/1.524577
[120] M. Marcu, ”The representations of spl(2, 1) – an example of representations of basic superalgebras,” J. Math. Phys.,21, No. 6, 1277–1283 (1980). · Zbl 0449.17001 · doi:10.1063/1.524576
[121] Y. Ne’eman and J. Tierry-Mieg, ”Gange asthenodynamics (SU(2/1)). Classical discussion,” Lect. Notes Math.,836, 318–348 (1980). · doi:10.1007/BFb0089747
[122] Tch. D. Palev, ”Canonical realizations of Lie superalgebras: ladder representations of the Lie superalgebra A(m, n),” J. Math. Phys.,22, No. 10, 2127–2131 (1981). · Zbl 0466.17006 · doi:10.1063/1.524781
[123] Tch. D. Palev, ”Fock space representations of the Lie superalgebra A(o, n),” J. Math. Phys.,21, No. 6, 1293–1298 (1980). · Zbl 0446.17003 · doi:10.1063/1.524578
[124] Tch. D. Palev, ”On a class of nontypical representations of the Lie superalgebra A(1, 0),” Godishn. Vyssh. Uchebn. Zaved., Tekh. Fiz., 1979,16, 103–104 (1980). · Zbl 0479.17002
[125] M. Parker, ”Real forms of simple finite-dimensional classical Lie superalgebras,” J. Math. Phys.,21, No. 4, 689–697 (1980). · Zbl 0445.17002 · doi:10.1063/1.524487
[126] P. Ramond and J. Schwarz, ”Classification of dual model gauge algebras,” Phys. Lett.,B64, No. 1, 75–77 (1976). · doi:10.1016/0370-2693(76)90361-0
[127] V. Rittenberg and M. Schennert, ”Elementary construction of graded Lie groups,” J. Math. Phys.,19, No. 3, 709–713 (1978). · Zbl 0374.22012 · doi:10.1063/1.523689
[128] V. Rittenberg and M. Schennert, ”A remarkable connection between the representations of the Lie superalgebras Osp (1, 2n) and the Lie algebras 0 (2n+1),” Comm. Math. Phys.,83, 1–9 (1982). · Zbl 0479.17001 · doi:10.1007/BF01947067
[129] V. Rittenberg and D. Wyler, ”Sequence of Z2 Z2-graded Lie algebras and superalgebras,” J. Math. Phys.,19, No. 10, 2193–2200 (1978). · Zbl 0423.17004 · doi:10.1063/1.523552
[130] M. Scheunert, ”The theory of Lie superalgebras,” Lect. Notes Math.,716 (1979). · Zbl 0407.17001
[131] A. N. Sergeev, ”The centre of enveloping algebra for Lie superalgebra Q(n, C),” Lett. Math. Phys.,7, 177–179 (1983). · Zbl 0539.17003 · doi:10.1007/BF00400431
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.