Double Lie algebras of a nonzero weight

Double Lie algebras of a nonzero weight Full article

Journal

Advances in Mathematics
ISSN: 0001-8708 , E-ISSN: 1090-2082

Output data

Year: 2022, Volume: 409, Article number : 108680, Pages count : DOI: 10.1016/j.aim.2022.108680

Tags

Double Lie algebra; Matrix algebra; Modified double Poisson algebra; Rota—Baxter operator

Authors

Goncharov M. ^1,2 , Gubarev V. ^1,2

Affiliations

1	Sobolev Institute of Mathematics, Acad. Koptyug ave. 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russian Federation

Funding (1)

Russian Science Foundation

21-11-00286

We introduce the notion of λ-double Lie algebra, which coincides with usual double Lie algebra when λ=0. We show that every λ-double Lie algebra for λ≠0 provides the structure of modified double Poisson algebra on the free associative algebra. In particular, it confirms the conjecture of S. Arthamonov (2017). We prove that there are no simple finite-dimensional λ-double Lie algebras. © 2022 Elsevier Inc.

Goncharov M. , Gubarev V.
Double Lie algebras of a nonzero weight
Advances in Mathematics. 2022. V.409. 108680 . DOI: 10.1016/j.aim.2022.108680 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000866224600005
Scopus:	2-s2.0-85137709398
Elibrary:	58829672
OpenAlex:	W3158136535

DB	Citing
Scopus	8
Web of science	7
OpenAlex	7