×

zbMATH — the first resource for mathematics

Steinberg conformal superalgebras. (English. Russian original) Zbl 1201.17014
J. Math. Sci., New York 152, No. 2, 268-273 (2008); translation from Fundam. Prikl. Mat. 12, No. 8, 189-196 (2006).
The authors continue their previous papers on universal central extensions of Lie conformal algebras: Vestn. Mosk. Univ., Ser. I 2005, No. 1, 26–31 (2005); translation in Mosc. Univ. Math. Bull. 60, No. 1, 26–31 (2005; Zbl 1101.17017), Fundam. Prikl. Mat. 11, No. 2, 135–155 (2005); translation in J. Math. Sci., New York 142, No. 2, 1954–1968 (2007; Zbl 1072.17011), and Sb. Math. 196, No. 5, 649–671 (2005); translation from Mat. Sb. 196, No. 5, 31–52 (2005; Zbl 1096.17008).
In this paper they describe the Steinberg conformal superalgebra as an abstract algebra by generators and relations.
MSC:
17B65 Infinite-dimensional Lie (super)algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] S. Bloch, ”The dilogarithm and extensions of Lie algebras,” in: Algebraic K-Theory. Proc. Conf., Evanston 1980, Lect. Notes Math., Vol. 854, Springer (1981), pp. 1–23.
[2] L. A. Bokut’, Y. Fong, and W.-F. Ke, ”Gröbner-Shirshov bases and the composition lemma for associative conformal algebras: An example,” in: K. Y. Chan, ed., Combinatorial and Computational Algebra. Int. Conf. on Combinatorial and Computational Algebra, May 24–29, 1999, Hong Kong, China, Contemp. Math., Vol. 264, Amer. Math. Soc., Providence (2000), pp. 63–90. · Zbl 1063.16031
[3] K. Iohara and Y. Kogti, ”Central extensions of Lie superalgebras,” Comment. Math. Helv., 76, 110–154 (2001). · Zbl 1036.17004 · doi:10.1007/s000140050152
[4] V. Kac, ”Lie superalgebras,” Adv. Math., 26, No. 1, 8–96 (1977). · Zbl 0366.17012 · doi:10.1016/0001-8708(77)90017-2
[5] V. Kac, Vertex Algebras for Beginners, Univ. Lect. Ser., Vol. 10, Amer. Math. Soc., Providence (1996). · Zbl 0861.17017
[6] C. Kassel, ”Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra,” J. Pure Appl. Algebra, 34, 265–275 (1984). · Zbl 0549.17009 · doi:10.1016/0022-4049(84)90040-9
[7] C. Kassel and J.-L. Loday, ”Extensions centrales d’algèbres de Lie,” Ann. Inst. Fourier, 32, 119–142 (1982). · Zbl 0485.17006
[8] A. V. Mikhalev and I. A. Pinchuk, ”Universal central extensions of an exceptional Lie superalgebra with nondegenerate Killing form,” in: Universal Algebra and Its Applications [in Russian], Peremena, Volgograd (2000), pp. 201–221.
[9] A. V. Mikhalev and I. A. Pinchuk, ”Universal central extensions of Lie superalgebras,” in: Formal Power Series and Algebraic Combinatorics. 12th Int. Conf., MAX Press, Moscow (2000), pp. 49–50. · Zbl 1135.17301
[10] A. V. Mikhalev and I. A. Pinchuk, ”Universal central extensions of the matrix Lie superalgebras sl(m, n, A),” in: K. Y. Chan, ed., Combinatorial and Computational Algebra. Int. Conf. on Combinatorial and Computational Algebra, May 24–29, 1999, Hong Kong, China, Contemp. Math., Vol. 264, Amer. Math. Soc., Providence (2000), pp. 111–125. · Zbl 1135.17301
[11] A. V. Mikhalev and I. A. Pinchuk, ”Universal central extensions of Lie superalgebras,” Tr. Sem. Petrovsk., 22, 261–282 (2002).
[12] A. V. Mikhalev and I. A. Pinchuk, ”Automorphisms and derivations of Lie conformal algebras and their universal extensions,” Chebyshevskii Sb., 5, No. 4, 98–114 (2004). · Zbl 1136.17022
[13] A. V. Mikhalev and I. A. Pinchuk, ”Conformal Lie algebras,” Mat. Sb., 196, No. 5, 32–52 (2005). · Zbl 1072.17011
[14] A. V. Mikhalev and I. A. Pinchuk, ”Steinberg unitary Lie conformal algebras,” Fundam. Prikl. Mat., 11, No. 2, 135–155 (2005). · Zbl 1072.17011
[15] A. V. Mikhalev and I. A. Pinchuk, ”Universal central extensions of Lie conformal algebras,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 1, 26–31 (2005). · Zbl 1101.17017
[16] J. Milnor, ”Introduction to algebraic K-theory,” Princeton Univ. Press, Princeton (1971). · Zbl 0237.18005
[17] E. Neher, ”An introduction to universal central extensions of Lie superalgebras,” in: Yu. Bahturin, ed., Groups, Rings, Lie and Hopf Algebras. Based on the Int. Workshop, St. John’s, Canada, May 28–June 1, 2001, Math. Its Appl., Vol. 555, Kluwer Academic, Dordrecht (2003), pp. 141–166.
[18] R. Steinberg, ”Générateurs, rélations et revêtements de groupes algébriques,” in: Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962), Librarie Universitaire, Louvain (1962), pp. 113–127.
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.