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Dimension formula for graded Lie algebras and its applications

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Authors
Kang, Seok-Jin; Kim, Myung-Hwan
Issue Date
1999
Publisher
American Mathematical Society
Citation
Trans. Amer. Math. Soc. 351 (1999), 4281-4336
Keywords
graded Lie algebrasDimension formula
Abstract
In this paper, we investigate the structure of in nite dimensional
Lie algebras L =
L
2􀀀 L graded by a countable abelian semigroup 􀀀 sat-
isfying a certain niteness condition. The Euler-Poincar e principle yields the
denominator identities for the 􀀀-graded Lie algebras, from which we derive a
dimension formula for the homogeneous subspaces L ( 2 􀀀). Our dimen-
sion formula enables us to study the structure of the 􀀀-graded Lie algebras in
a uni ed way. We will discuss some interesting applications of our dimension
formula to the various classes of graded Lie algebras such as free Lie algebras,
Kac-Moody algebras, and generalized Kac-Moody algebras. We will also dis-
cuss the relation of graded Lie algebras and the product identities for formal
power series.
ISSN
0065-9290
Language
English
URI
https://hdl.handle.net/10371/12178
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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