Lie algebra configuration pairing

Details Lie algebra configuration pairing Lie algebra configuration pairing

2010-10-22

arxiv.org/abs/1010.4732v1

Mathematics

Rings and Algebras

14 pages; uses xypic

Scientific paper

We give a new description of the configuration pairing of Sinha and Walter by showing that it computes coefficients in the associative, preLie, or graph polynomial of a Lie bracket expression. We also connect the graph complexes of Sinha and Walter with preLie algebras. Examples apply the combinatorial definition of the configuration pairing to compute coefficients in the associative (noncommutative) polynomial of Lie elements. This outlines a new way of understanding and computing with Lie algebras.

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