zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Representation rings of Lie superalgebras. (English) Zbl 1122.19001
The author studies representation rings of Lie superalgebras and introduces several variants and possible definitions of the representation ring. The author also constructs representation groups built from ungraded g-modules, as well as degree-shifted representation groups using Clifford modules.

19A22Frobenius induction, Burnside and representation rings
19L47Equivariant $K$-theory
17B10Representations of Lie algebras, algebraic theory
16E20Grothendieck groups and $K$-theory of noncommutative rings
Full Text: DOI
[1] · Zbl 0146.19101 · doi:10.1093/qmath/17.1.367
[2] · Zbl 0146.19001 · doi:10.1016/0040-9383(64)90003-5
[3] Atiyah, M. F. and Hopkins, M.: A variant of K-theory: K {$\pm$} . Topology, Geometry and Quantum Field Theory, London Math. Soc. Lecture Note Ser., 308, Cambridge Univ. Press, Cambridge, 2004, pp. 5--17, arXiv:math.KT/0302128.
[5] Bott, R.: The index theorem for homogeneous differential operators. Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, NJ, 1965, pp. 167--186.
[6] Bott, R.: On induced representations. The Mathematical Heritage of Hermann Weyl (Durham, NC, 1987), Proc. Sympos. Pure Math., 48, Amer. Math. Soc., Providence, RI, 1988, pp. 1--13.
[7] Brundan, J. and Kleshchev, A.: Hecke-Clifford superalgebras, crystals of type $A^{2l}_{(2)}$ and modular branching rules for $\hat{S}_n$ . Represent. Theory 5 (2001), 317--403 (electronic). arXiv:math.RT/0103060. · Zbl 1005.17010
[8] · Zbl 1029.20008 · doi:10.1007/s002090100282
[9] · Zbl 0207.22003 · doi:10.1007/BF02684650
[10] Freed, D.: Twisted K-theory and loop groups. Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), Higher Ed. Press, Beijing, 2002, pp. 419--430, arXiv:math.AT/0206257. · Zbl 0997.19004
[11] Freed, D., Hopkins, M. and Teleman, C.: Twisted K-theory and loop group representations I. arXiv:math.AT/ 0312155. · Zbl 1241.19002
[12] Freed, D., Hopkins, M. and Teleman, C.: Twisted equivariant K-theory with complex coefficients. arXiv:math.AT/ 0206257. · Zbl 1188.19005
[13] · doi:10.1016/S0370-2693(97)01505-0
[14] Gross, B., Kostant, B., Ramond, P. and Sternberg, S.: The Weyl character formula, the half-spin representations, and equal rank subgroups, Proc. Natl. Acad. Sci. USA 95(15) (1998), 8441--8442 (electronic). arXiv:math.RT/9808133. · Zbl 0918.17002
[15] · Zbl 0359.17009 · doi:10.1007/BF01609166
[16] · Zbl 0366.17012 · doi:10.1016/0001-8708(77)90017-2
[17] Karoubi, M.: K-theory. An introduction. Grundlehren der Mathematischen Wissenschaften, Band 226. Springer-Verlag, Berlin-New York, 1978. xviii+308 pp. ISBN: 3-540-08090-2. · Zbl 0382.55002
[18] · Zbl 0952.17005 · doi:10.1215/S0012-7094-99-10016-0
[19] · Zbl 0972.22008 · doi:10.1090/S1088-4165-00-00102-3
[20] · Zbl 1018.17016 · doi:10.1215/S0012-7094-01-11014-4
[21] · Zbl 1090.19001 · doi:10.1016/j.jpaa.2005.04.001
[23] Leites, D. (ed.): Seminar on supersymmetries. Preprint, 1983--2005.
[24] · Zbl 0163.28202 · doi:10.2307/1970615
[25] Serganova, V. V.: Classification of simple real Lie superalgebras and symmetric superspaces. (Russian) Funktsional. Anal. i Prilozhen. 17(3) (1983), 46--54; English translation: Functional Anal. Appl. 17(3) (1983), 200--207.
[26] · Zbl 1002.17002 · doi:10.1307/mmj/1008719038
[27] Shchepochkina, I.: Maximal subalgebras of the classical linear Lie superalgebras. The Orbit Method in Geometry and Physics (Marseille, 2000), Progr. Math., 213, Birkhäuser Boston, Boston, MA, 2003, pp. 445--472. arXiv:hep-th/9702122. · Zbl 1080.17004