The configuration basis of a Lie algebra and its dual

Details The configuration basis of a Lie algebra and its dual The configuration basis of a Lie algebra and its dual

2010-10-22

arxiv.org/abs/1010.4765v1

Mathematics

Rings and Algebras

15 pages; uses xypic

Scientific paper

We use the Lie coalgebra and configuration pairing framework presented previously by Sinha and Walter to derive a new, left-normed monomial basis for free Lie algebras (built from associative Lyndon-Shirshov words), as well as a dual monomial basis for Lie coalgebras. Our focus is on computational dexterity gained by using the configuration framework and basis. We include several explicit examples using the dual coalgebra basis and configuration pairing to perform Lie algebra computations. As a corollary of our work, we get a new multiplicative basis for the shuffle algebra.

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