Involve: A Journal of Mathematics
- Volume 9, Number 5 (2016), 783-795.
The left greedy Lie algebra basis and star graphs
We construct a basis for free Lie algebras via a left greedy bracketing algorithm on Lyndon–Shirshov words. We use a new tool — the configuration pairing between Lie brackets and graphs of Sinha and Walter — to show that the left greedy brackets form a basis. Our constructions further equip the left greedy brackets with a dual monomial Lie coalgebra basis of star graphs. We end with a brief example using the dual basis of star graphs in a Lie algebra computation.
Involve, Volume 9, Number 5 (2016), 783-795.
Received: 29 April 2015
Revised: 23 October 2015
Accepted: 27 October 2015
First available in Project Euclid: 22 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 17B35: Universal enveloping (super)algebras [See also 16S30]
Secondary: 17B62: Lie bialgebras; Lie coalgebras 16T15: Coalgebras and comodules; corings 18D50: Operads [See also 55P48]
Walter, Benjamin; Shiri, Aminreza. The left greedy Lie algebra basis and star graphs. Involve 9 (2016), no. 5, 783--795. doi:10.2140/involve.2016.9.783. https://projecteuclid.org/euclid.involve/1511371069