Double Lie algebras of a nonzero weight

Maxim Goncharov; Vsevolod Gubarev

doi:10.1016/j.aim.2022.108680

Double Lie algebras of a nonzero weight

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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.

Original language	English
Article number	108680
Journal	Advances in Mathematics
Volume	409
DOIs	https://doi.org/10.1016/j.aim.2022.108680
Publication status	Published - 19 Nov 2022

Keywords

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

OECD FOS+WOS

1.01 MATHEMATICS

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10.1016/j.aim.2022.108680

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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",

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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.

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KW - Matrix algebra

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KW - Rota—Baxter operator

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Double Lie algebras of a nonzero weight

Abstract

Keywords

OECD FOS+WOS

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