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Graded Lie superalgebras, supertrace formula,and orbit Lie superalgebras

Cited 29 time in Web of Science Cited 30 time in Scopus
Authors
Kang, Seok-Jin; Kwon, Jae-Hoon
Issue Date
2000
Publisher
Oxford University Press
Citation
Proc. London Math. Soc. (3) 81(2000) 675-724
Keywords
orbit Lie superalgebrasLie superalgebrassupertraces
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.
ISSN
0024-6115
Language
English
URI
https://hdl.handle.net/10371/12195
DOI
https://doi.org/10.1112/S0024611500012661
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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