学术报告Double Lie algebras of a nonzero weight
发布时间:2024-04-09
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报 告 人:
Maxim Goncharov 研究员 (索博列夫数学研究所)
时 间:
2024年4月13日(星期六)16:30-17:30
地 点:
理学楼402
主办单位:
理学院
联系人:
郎红蕾
联系方式:
hllang@cau.edu.cn
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The notion of a double Poisson algebra on a given associative algebra was introduced by M. Van den Bergh in 2008 as a noncommutative analog of Poisson algebra. The goal behind this notion was to develop noncommutative Poisson geometry. The notion of double Lie algebra (of weight zero) naturally arose directly from the definition of double Poisson algebra. In this talk, I will introduce the notion of a double Lie algebra of an arbitrary weight lambda, which coincides with the usual double Lie algebra when the weight lambda is equal to zero. I will focus on the algebraic and combinatorial ideas that lead us to the definition and on connections between structures of double Lie algebras and Rota-Baxter operators of special type on the corresponding matrix algebra. As a motivation, I will speak on the connection between lambda-double Lie algebra and structures of modified double Poisson algebra on the free associative algebra. Also, some properties of finite-dimensional lambda-double Lie algebras will be discussed.
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Maxim Goncharov, 索博列夫数学研究所高级研究员,新西伯利亚国立大学副教授。
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