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arXiv · 1510.06984

The left-greedy Lie algebra basis and star graphs

Benjamin Walter·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-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.

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Benjamin Walter, Aminreza Shiri. 2015-10-23. The left-greedy Lie algebra basis and star graphs. https://doi.org/10.2140/involve.2016.9.783

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