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Graded Lie superalgebras, supertrace formula,and orbit Lie superalgebras
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kang, Seok-Jin | - |
dc.contributor.author | Kwon, Jae-Hoon | - |
dc.date.accessioned | 2009-11-16T04:29:46Z | - |
dc.date.available | 2009-11-16T04:29:46Z | - |
dc.date.issued | 2000 | - |
dc.identifier.citation | Proc. London Math. Soc. (3) 81(2000) 675-724 | en |
dc.identifier.issn | 0024-6115 | - |
dc.identifier.uri | https://hdl.handle.net/10371/12195 | - |
dc.description.abstract | Let be a countable abelian semigroup and A be a countable abelian group satisfying a certain finiteness condition. Suppose that a group G acts on a x A-graded Lie superalgebra L = (, a) x A L(, a) by Lie superalgebra automorphisms preserving the x A-gradation. In this paper, we show that the Euler–Poincaré principle yields the generalized denominator identity for L and derive a closed form formula for the supertraces str(g| L(, a) for all g G, where (, a) x A. We discuss the applications of our supertrace formula to various classes of infinite-dimensional Lie superalgebras such as free Lie superalgebras and generalized Kac–Moody superalgebras. In particular, we determine the decomposition of free Lie superalgebras into a direct sum of irreducible GL(n) x GL(k)-modules, and the supertraces of the Monstrous Lie superalgebras with group actions. Finally, we prove that the generalized characters of Verma modules and irreducible highest-weight modules over a generalized Kac–Moody superalgebra g corresponding to the Dynkin diagram automorphism are the same as the usual characters of Verma modules and irreducible highest-weight modules over the orbit Lie superalgebra = g() determined by . 1991 Mathematics Subject Classification: 17A70, 17B01, 17B65, 17B70, 11F22. | en |
dc.language.iso | en | - |
dc.publisher | Oxford University Press | en |
dc.subject | orbit Lie superalgebras | en |
dc.subject | Lie superalgebras | en |
dc.subject | supertraces | en |
dc.title | Graded Lie superalgebras, supertrace formula,and orbit Lie superalgebras | en |
dc.type | Article | en |
dc.contributor.AlternativeAuthor | 강석진 | - |
dc.contributor.AlternativeAuthor | 권재훈 | - |
dc.identifier.doi | 10.1112/S0024611500012661 | - |
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