Vol. 9, No. 5, 2016

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The left greedy Lie algebra basis and star graphs

Benjamin Walter and Aminreza Shiri

Vol. 9 (2016), No. 5, 783–795
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.

Keywords
Lie algebra, bases, free Lie algebra
Mathematical Subject Classification 2010
Primary: 17B35
Secondary: 17B62, 16T15, 18D50
Milestones
Received: 29 April 2015
Revised: 23 October 2015
Accepted: 27 October 2015
Published: 25 August 2016

Communicated by Vadim Ponomarenko
Authors
Benjamin Walter
Department of Mathematics
Middle East Technical University
Northern Cyprus Campus
Kalkanli, Guzelyurt, KKTC
10 Mersin
Turkey
Aminreza Shiri
Department of Mathematics
Middle East Technical University
Northern Cyprus Campus
Kalkanli, Guzelyurt, KKTC
10 Mersin
Turkey