descriptionPublicationkeyboard_double_arrow_right Article , Preprint 05 Jul 2019Embargo end date: 01 Jan 2016 English Publisher:World Scientific Pub Co Pte LtdJournal:Journal of Algebra and Its Applications, volume 19, page 2,050,119 (issn: 0219-4988, eissn: 1793-6829,

Authors: Eduardo Eizo Aramaki Hitomi; Felipe Yukihide Yasumura;

doi: 10.1142/s0219498820501194 , 10.48550/arxiv.1609.09407

arXiv: http://arxiv.org/abs/1609.09407

On the combinatorics of commutators of Lie algebras

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Abstract

Motivated by the combinatorial properties of products in Lie algebras, we investigate the subset of permutations that naturally appears when we write the long commutator [Formula: see text] as a sum of associative monomials. We characterize this subset and find some useful equivalences. Moreover, we explore properties concerning the action of this subset on sequences of [Formula: see text] elements. In particular, we describe sequences that share some special symmetries which can be useful in the study of combinatorial properties in graded Lie algebras.

Related Organizations

State University of Campinas
Brazil
State University of Maringa
Brazil

Keywords

Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Combinatorics, 17B05, 05E18, Mathematics - Rings and Algebras, Combinatorics (math.CO)

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