Free Lie-admissible algebras and an analogue of the PBW theorem

Autor(es)

Chen, Yuqun ^[1] ; Shestakov, Ivan ^{[2, 3]} ; Zhang, Zerui ^[1]

Afiliação do(s) autor(es)

^[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631 - Peoples R China

^[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

^[3] Sobolev Inst Math, Novosibirsk - Russia

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 590, p. 234-253, JAN 15 2022.
• Citações Web of Science: 0

Resumo

We first construct linear bases for free Lie-admissible algebras and develop a new theory of Griibner-Shirshov bases for Lie-admissible algebras. Then we prove an analogue of the Poincare-Birkhoff-Witt theorem, that is, every Lie algebra L can be embedded into its universal enveloping Lie-admissible algebra U(L), where the basis of U(L) does not depend on the multiplication table of L. Finally, we show that the basic rank of the variety of Lie-admissible algebras is 1. As a corollary, the universal enveloping Lie-admissible algebra of an abelian Lie algebra does not satisfy any nontrivial identity in the variety of Lie-admissible algebras. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático