• 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}
}
  • Ben Walter
  • Published 22 October 2010
  • Mathematics
  • arXiv: Rings and Algebras
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… 

Figures from this paper

References

SHOWING 1-10 OF 15 REFERENCES
Lie algebra configuration pairing
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
A right normed basis for free Lie algebras and Lyndon–Shirshov words
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 ] … ] ] ] ,
Lie coalgebras and rational homotopy theory, I: graph coalgebras
In this paper we develop a new, computationally friendly approach to Lie coalgebras through graph coalgebras, and we apply this approach to Harrison homology. There are two standard to presentations
A pairing between graphs and trees
We develop a canonical pairing between trees and graphs, which passes to their quotients by Jacobi identities. This pairing is an effective and simple tool for understanding the Lie and Poisson
Lie coalgebras and rational homotopy theory, I
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
Free Lie Algebras
Lyndon words, free algebras and shuffles
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
...
1
2
...