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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 17B35
Secondary: 17B62, 16T15, 18D50
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Milestones
Received: 29 April 2015
Revised: 23 October 2015
Accepted: 27 October 2015
Published: 25 August 2016
Communicated by Vadim Ponomarenko
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Authors |
| Benjamin Walter | |
| Department of Mathematics Middle East Technical University Northern Cyprus Campus Kalkanli, Guzelyurt, KKTC 10 Mersin Turkey |
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| Aminreza Shiri | |
| Department of Mathematics Middle East Technical University Northern Cyprus Campus Kalkanli, Guzelyurt, KKTC 10 Mersin Turkey |
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