A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras
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：白承铭（南开大学陈省身数学研究所）
：2023-12-29 14:30
：海韵园实验楼105报告厅
报告人：白承铭（南开大学陈省身数学研究所）
时 间：2023年12月29日14:30
地 点：海韵园实验楼105报告厅
内容摘要:
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.
个人简介：
白承铭，南开大学陈省身数学研究所教授，所长，国务院学位委员会第八届学科评议组成员，教育部核心数学与组合数学重点实验室主任，物理中的群论方法国际大会常务委员会委员。主要从事与数学物理和李理论相关的一些代数体系的结构及其应用的研究。曾获国家杰出青年基金资助和国务院政府特殊津贴，培养博士生和硕士生多名。其中，倪翔曾获中国数学会“钟家庆数学奖优秀硕士论文奖”。
联系人：王清
