RUS  ENG
Полная версия
ЖУРНАЛЫ // Сибирские электронные математические известия // Архив

Сиб. электрон. матем. изв., 2024, том 21, выпуск 1, страницы 81–97 (Mi semr1670)

Математическая логика, алгебра и теория чисел

On connection between Rota—Baxter operators and solutions of the classical Yang—Baxter equation with an ad-invariant symmetric part on general linear algebra

M. E. Goncharov

Sobolev Institute of Mathematics, Academician Koptyug avenue, 4, 630090, Novosibirsk, Russia

Аннотация: In the paper, we find the connection between solutions of the classical Yang—Baxter equation with an ad-invariant symmetric part and Rota—Baxter operators of special type on a real general linear algebra $gl_n(\mathbb R)$. Using this connection, we classify solutions of the classical Yang—Baxter equation with an ad-invariant symmetric part on $gl_2(\mathbb C)$ using the classification of Rota—Baxter operators of nonzero weight on $gl_2(\mathbb C)$ and a classification of Rota—Baxter operators of weight 0 on $sl_2(\mathbb C)$.

Ключевые слова: Lie bialgebra, Rota—Baxter operator, classical Yang—Baxter equation, general linear Lie algebra.

УДК: 512.554

MSC: 17B38

Поступила 14 августа 2023 г., опубликована 14 февраля 2024 г.

Язык публикации: английский

DOI: doi.org/10.33048/semi.2024.21.007



© МИАН, 2024