Advanced search
Start date
Betweenand
Related content
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

Full text
Author(s):
Chen, Yuqun [1] ; Shestakov, Ivan [2, 3] ; Zhang, Zerui [1]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: Journal of Algebra; v. 590, p. 234-253, JAN 15 2022.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
Grantee:Ivan Chestakov
Support Opportunities: Research Projects - Thematic Grants