報告題目：A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras
報 告 人：Chengming Bai
所在單位：南開大學陳省身數學研究所
報告時間：2024年8月13日 15:00-16:00
報告地點：吉林大學數學樓第5研讨室
報告摘要: The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is not available for giving a bialgebra theory for transposed Poisson algebras. Alternatively, we consider Manin triples with respect to the commutative 2-cocycles on the Lie algebras instead. Explicitly, we first introduce the notion of anti-pre-Lie bialgebras as the equivalent structure of Manin triples of Lie algebras with respect to the commutative 2-cocycles. Then we introduce the notion of anti-pre-Lie Poisson bialgebras, characterized by Manin triples of transposed Poisson algebras with respect to the bilinear forms which are invariant on the commutative associative algebras and commutative 2-cocycles on the Lie algebras, giving a bialgebra theory for transposed Poisson algebras. This is a joint work with Guilai Liu.
報告人簡介：白承銘，南開大學陳省身數學研究所教授，所長，南開大學副校長，國務院學位委員會第八屆學科評議組成員，教育部核心數學與組合數學重點實驗室主任，物理中的群論方法國際大會常務委員會委員。主要從事與數學物理和李理論相關的一些代數體系的結構及其應用的研究。曾獲國家傑出青年基金資助和國務院政府特殊津貼，并入選國家“萬人計劃”科技創新領軍人才。培養博士生和碩士生多名，其中的倪翔曾獲中國數學會“鐘家慶數學獎優秀碩士論文獎”。
