Browse

Free Lie algebras, generalized Witt formula, and the denominator identity

Cited 20 time in Web of Science Cited 24 time in Scopus
Authors
Kang, Seok-Jin; Kim, Myung-Hwan
Issue Date
1996
Publisher
Elsevier
Citation
J. Algebra 183 (1996), 560-594
Abstract
Let G be a countable abelian semigroup satisfying a suitable finiteness condition, and let L= directsum of L_a be the free Lie algebra generated by a G-graded vector space V over C. In this paper, from the denominator identity, we derive a dimension formula for the homogeneous subspaces of the free Lie algebra L= directsum of L_a and discuss numerous applications of our dimension formula to various interesting cases. Our dimension formula will be expressed in terms of the Witt partition functions. Various expressions of the Witt partition functions will give rise to a number of interesting combinatorial identities. As a special case, we obtain a recursive relation for the coefficients of the elliptic modular function j.
ISSN
0021-8693
Language
English
URI
https://hdl.handle.net/10371/12192
DOI
https://doi.org/10.1006/jabr.1996.0233
Files in This Item:
There are no files associated with this item.
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
  • mendeley

Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

Browse