M. E. Goncharov, “On Rota–Baxter operators of non-zero weight arisen from the solutions of the classical Yang–Baxter equation”, Сиб. электрон. матем. изв., 2017, том 14,страницы 1533

Эта публикация цитируется в 3 статьях

Математическая логика, алгебра и теория чисел

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

M. E. Goncharov^ab

^a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Department of Mechanics and Mathematics, Novosibirsk State University, Russia

Аннотация: 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.

Ключевые слова: Rota–Baxter operator, anti-commutative algebra, Lie algebra, Malcev algebra, non-associative bialgebra, classical Yang–Baxter equation.

УДК: 512.554

MSC: 16T25,17B62,17D10,17A36

Поступила 27 октября 2017 г., опубликована 29 декабря 2017 г.

Язык публикации: английский

DOI: 10.17377/semi.2017.14.132