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Graded Lie superalgebras, supertrace formula,and orbit Lie superalgebras

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dc.contributor.authorKang, Seok-Jin-
dc.contributor.authorKwon, Jae-Hoon-
dc.date.accessioned2009-11-16T04:29:46Z-
dc.date.available2009-11-16T04:29:46Z-
dc.date.issued2000-
dc.identifier.citationProc. London Math. Soc. (3) 81(2000) 675-724en
dc.identifier.issn0024-6115-
dc.identifier.urihttps://hdl.handle.net/10371/12195-
dc.description.abstractLet 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.isoen-
dc.publisherOxford University Pressen
dc.subjectorbit Lie superalgebrasen
dc.subjectLie superalgebrasen
dc.subjectsupertracesen
dc.titleGraded Lie superalgebras, supertrace formula,and orbit Lie superalgebrasen
dc.typeArticleen
dc.contributor.AlternativeAuthor강석진-
dc.contributor.AlternativeAuthor권재훈-
dc.identifier.doi10.1112/S0024611500012661-
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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