Double Lie algebras of a nonzero weight

Standard

Double Lie algebras of a nonzero weight. / Goncharov, Maxim ; Gubarev, Vsevolod.

In: Advances in Mathematics, Vol. 409, 108680, 19.11.2022.

Research output: Contribution to journal › Article › peer-review

Harvard

Goncharov, M & Gubarev, V 2022, 'Double Lie algebras of a nonzero weight', Advances in Mathematics, vol. 409, 108680. https://doi.org/10.1016/j.aim.2022.108680

APA

Goncharov, M., & Gubarev, V. (2022). Double Lie algebras of a nonzero weight. Advances in Mathematics, 409, [108680]. https://doi.org/10.1016/j.aim.2022.108680

Vancouver

Goncharov M , Gubarev V. Double Lie algebras of a nonzero weight. Advances in Mathematics. 2022 Nov 19;409:108680. doi: 10.1016/j.aim.2022.108680

Author

Goncharov, Maxim ; Gubarev, Vsevolod. / Double Lie algebras of a nonzero weight. In: Advances in Mathematics. 2022 ; Vol. 409.

BibTeX

@article{16e1d92f2dd04d7abd319ceed6058bec,

title = "Double Lie algebras of a nonzero weight",

abstract = "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.",

keywords = "Double Lie algebra, Matrix algebra, Modified double Poisson algebra, Rota—Baxter operator",

author = "Maxim Goncharov and Vsevolod Gubarev",

note = "Funding Information: The research is supported by Russian Science Foundation (project 21-11-00286 ). Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = nov,

day = "19",

doi = "10.1016/j.aim.2022.108680",

language = "English",

volume = "409",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Double Lie algebras of a nonzero weight

AU - Goncharov, Maxim

AU - Gubarev, Vsevolod

PY - 2022/11/19

Y1 - 2022/11/19

N2 - 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.

AB - 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.

KW - Double Lie algebra

KW - Matrix algebra

KW - Modified double Poisson algebra

KW - Rota—Baxter operator

UR - http://www.scopus.com/inward/record.url?scp=85137709398&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2022.108680

DO - 10.1016/j.aim.2022.108680

M3 - Article

AN - SCOPUS:85137709398

VL - 409

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 108680

ER -

ID: 38037050