On Rota-Baxter operators of non-zero weight arisen from the solutions of the classical Yang-Baxter equation

Maxim Goncharov

doi:10.17377/semi.2017.14.132

On Rota-Baxter operators of non-zero weight arisen from the solutions of the classical Yang-Baxter equation

Maxim Goncharov

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

4 Citations (Scopus)

Abstract

Let L be a simple anti-commutative algebra. In this paper we prove that a non skew-symmetric solution of the classical Yang- Baxter equation on L with L-invariant symmetric part induces on L a Rota-Baxter operator of a non-zero weight.

Original language	English
Pages (from-to)	1533-1544
Number of pages	12
Journal	Сибирские электронные математические известия
Volume	14
DOIs	https://doi.org/10.17377/semi.2017.14.132
Publication status	Published - 1 Jan 2017

Keywords

Anti-commutative algebra
Classical Yang-Baxter equation
Lie algebra
Malcev algebra
Non-associative bialgebra
Rota-Baxter operator
non-associative bialgebra
ALGEBRAS
classical Yang-Baxter equation
anti-commutative algebra
BIALGEBRAS

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10.17377/semi.2017.14.132

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title = "On Rota-Baxter operators of non-zero weight arisen from the solutions of the classical Yang-Baxter equation",

abstract = "Let L be a simple anti-commutative algebra. In this paper we prove that a non skew-symmetric solution of the classical Yang- Baxter equation on L with L-invariant symmetric part induces on L a Rota-Baxter operator of a non-zero weight.",

keywords = "Anti-commutative algebra, Classical Yang-Baxter equation, Lie algebra, Malcev algebra, Non-associative bialgebra, Rota-Baxter operator, non-associative bialgebra, ALGEBRAS, classical Yang-Baxter equation, anti-commutative algebra, BIALGEBRAS",

author = "Maxim Goncharov",

year = "2017",

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doi = "10.17377/semi.2017.14.132",

language = "English",

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N2 - Let L be a simple anti-commutative algebra. In this paper we prove that a non skew-symmetric solution of the classical Yang- Baxter equation on L with L-invariant symmetric part induces on L a Rota-Baxter operator of a non-zero weight.

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KW - Anti-commutative algebra

KW - Classical Yang-Baxter equation

KW - Lie algebra

KW - Malcev algebra

KW - Non-associative bialgebra

KW - Rota-Baxter operator

KW - non-associative bialgebra

KW - ALGEBRAS

KW - classical Yang-Baxter equation

KW - anti-commutative algebra

KW - BIALGEBRAS

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DO - 10.17377/semi.2017.14.132

M3 - Article

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VL - 14

SP - 1533

EP - 1544

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

On Rota-Baxter operators of non-zero weight arisen from the solutions of the classical Yang-Baxter equation

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Keywords

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