Transactions of the American Mathematical Society

Author(s): Seok-Jin Kang; Myung-Hwan Kim
Journal: Trans. Amer. Math. Soc. 351 (1999), 4281-4336.
MSC (1991): Primary 17B01, 17B65, 17B70, 11F22
Posted: June 29, 1999
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Abstract: In this paper, we investigate the structure of infinite dimensional Lie algebras $L=\bigoplus _{\alpha \in \Gamma } L_{\alpha }$ graded by a countable abelian semigroup $\Gamma$ satisfying a certain finiteness condition. The Euler-Poincaré principle yields the denominator identities for the $\Gamma$ -graded Lie algebras, from which we derive a dimension formula for the homogeneous subspaces $L_{\alpha }$ $(\alpha \in \Gamma )$ . Our dimension formula enables us to study the structure of the $\Gamma$ -graded Lie algebras in a unified 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 discuss the relation of graded Lie algebras and the product identities for formal power series.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 17B01, 17B65, 17B70, 11F22

Seok-Jin Kang
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Email: sjkang@math.snu.ac.kr

Myung-Hwan Kim
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Email: mhkim@math.snu.ac.kr

DOI: 10.1090/S0002-9947-99-02239-4
PII: S 0002-9947(99)02239-4
Received by editor(s): May 23, 1997
Posted: June 29, 1999
Additional Notes: This research was supported by NON DIRECTED RESEARCH FUND, Korea Research Foundation, 1996.
Copyright of article: Copyright 1999, American Mathematical Society

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