 

M. P. de Oliveira
On Commutation Relations for 3Graded Lie Algebras


Published: 
September 5, 2001 
Keywords: 
3graded Lie algebras, kernel functions 
Subject: 
17B70, 16W10 


Abstract
We prove some commutation relations for a 3graded Lie algebra,
i.e., a Zgraded
Lie algebra whose nonzero homogeneous
elements have degrees
1, 0 or 1, over a field K. In particular, we examine the
free 3graded
Lie algebra generated by an element of degree 1 and another of degree 1. We show
that if K has characteristic zero,
such a Lie algebra can be realized as a Lie algebra
of matrices over polynomials in one indeterminate.
In the end, we apply the results obtained to derive
the classical commutation relations for elements in the universal
enveloping algebra of
sl_{2}(K).


Author information
Department of Mathematics and Statistics, University of Sao Paulo, Brazil
marcelo@ime.usp.br

