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Corpus ID: 118311837

The configuration basis of a Lie algebra and its dual

@article{Walter2010TheCB,
title={The configuration basis of a Lie algebra and its dual},
author={Ben Walter},
journal={arXiv: Rings and Algebras},
year={2010}
}

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… Expand

We give an algebraic construction of the topological graph-tree configuration pairing of Sinha and Walter beginning with the classical presentation of Lie coalgebras via coefficients of words in the… Expand

Abstract In this article we construct a basis of a free Lie algebra that consists of right normed words, i.e. the words that have the following form: [ a i 1 [ a i 2 [ … [ a i t − 1 a i t ] … ] ] ] ,… Expand

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In this paper we complete the picture of Lie and commutative algebra and coalgebra models for rational spaces by giving a new, combinatorially rich Lie coalgebra model. Consider the following square… Expand

1. Introduction. A Lyndon word is a primitive word which is minimum in its conjugation class, for the lexicographical ordering. These words have been introduced by Lyndon in order to find bases of… Expand