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Graded Lie superalgebras and the superdimension formula

Cited 19 time in Web of Science Cited 23 time in Scopus
Authors
Seok-Jin, Kang
Issue Date
1998
Publisher
Elsevier
Citation
J. Algebra 204 (1998), 597-655
Keywords
Graded Lie superalgebrassuperdimension formula
Abstract
In this paper, we investigate the structure of graded Lie superalgebras = (, a) × (, a), where is a countable abelian semigroup and is a countable abelian group with a coloring map satisfying a certain finiteness condition. Given a denominator identity for the graded Lie superalgebra , we derive a superdimension formula for the homogeneous subspaces (, a) ( , a ), which enables us to study the structure of graded Lie superalgebras in a unified way. We discuss the applications of our superdimension formula to free Lie superalgebras, generalized Kac–Moody superalgebras, and Monstrous Lie superalgebras. In particular, the product identities for normalized formal power series are interpreted as the denominator identities for free Lie superalgebras. We also give a characterization of replicable functions in terms of product identities and determine the root multiplicities of Monstrous Lie superalgebras.
ISSN
0021-8693
Language
English
URI
http://hdl.handle.net/10371/13503
DOI
https://doi.org/10.1006/jabr.1997.7352
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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