Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 5 (2016), 783-795.

The left greedy Lie algebra basis and star graphs

Benjamin Walter and Aminreza Shiri

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Abstract

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.

Article information

Source
Involve, Volume 9, Number 5 (2016), 783-795.

Dates
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
https://projecteuclid.org/euclid.involve/1511371069

Digital Object Identifier
doi:10.2140/involve.2016.9.783

Mathematical Reviews number (MathSciNet)
MR3541979

Zentralblatt MATH identifier
1383.17004

Subjects
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]

Keywords
Lie algebra bases free Lie algebra

Citation

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


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References

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