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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.
Поступила 14 августа 2023 г., опубликована 14 февраля 2024 г.
Образец цитирования:
M. E. Goncharov, “On connection between Rota—Baxter operators and solutions of the classical Yang—Baxter equation with an ad-invariant symmetric part on general linear algebra”, Сиб. электрон. матем. изв., 21:1 (2024), 81–97
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1670 https://www.mathnet.ru/rus/semr/v21/i1/p81
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