An application of free Lie algebras to polynomial current algebras and their representation theory

2005 ◽  
pp. 15-31 ◽  
Author(s):  
Vyjayanthi Chari ◽  
Jacob Greenstein
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Free Lie Algebras ◽  
Current Algebras

WHITEHEAD EXACT SEQUENCE AND DIFFERENTIAL GRADED FREE LIE ALGEBRA

2004 ◽  
Vol 15 (10) ◽  
pp. 987-1005 ◽  
Author(s):  
MAHMOUD BENKHALIFA
Keyword(s):  
Exact Sequence ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Integral Domain ◽  
Free Lie Algebra ◽  
Universal Algebras ◽  
Free Lie Algebras ◽  
Equivalent Class

Let R be a principal and integral domain. We say that two differential graded free Lie algebras over R (free dgl for short) are weakly equivalent if and only if the homologies of their corresponding enveloping universal algebras are isomophic. This paper is devoted to the problem of how we can characterize the weakly equivalent class of a free dgl. Our tool to address this question is the Whitehead exact sequence. We show, under a certain condition, that two R-free dgls are weakly equivalent if and only if their Whitehead sequences are isomorphic.

scholarly journals Invariant Bases for Free Lie Algebras

1998 ◽  
Vol 204 (1) ◽  
pp. 337-346 ◽  
Author(s):  
Sean Guilfoyle ◽  
Ralph Stöhr
Keyword(s):  
Lie Algebras ◽  
Free Lie Algebras
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