Title: A Bialgebra Theory for Transposed Poisson Algebras via Anti-pre-Lie Bialgebras and Anti-pre-Lie-Poisson Bialgebras
Speaker: Chengming Bai
Institution: Chern Institute of Mathematics, Nankai University
Date & Time: August 13, 2024, 15:00–16:00
Location: Seminar Room 5, Mathematics Building, Jilin University
The traditional approach to Poisson bialgebras, characterized by Manin triples with invariant bilinear forms on both commutative associative algebras and Lie algebras, does not directly extend to a bialgebra theory for transposed Poisson algebras. Instead, we introduce Manin triples with respect to commutative 2-cocycles on Lie algebras. Specifically, we first define
anti-pre-Lie bialgebras as the algebraic structure equivalent to Manin triples of Lie algebras with commutative 2-cocycles. We then introduce
anti-pre-Lie-Poisson bialgebras, characterized by Manin triples of transposed Poisson algebras with bilinear forms that are invariant on commutative associative algebras and commutative 2-cocycles on Lie algebras. This framework establishes a systematic bialgebra theory for transposed Poisson algebras. Joint work with Guilai Liu.
Chengming Bai is a Professor and Director of the Chern Institute of Mathematics at Nankai University, serving also as Vice President of Nankai University. He is a member of the 8th Discipline Appraisal Group of the State Council, Director of the Key Laboratory of Core Mathematics and Combinatorics (MOE), and a Standing Committee Member of the International Conference on Group Theory Methods in Physics. His research focuses on algebraic structures in mathematical physics and Lie theory, with applications to integrable systems and quantum groups. A recipient of the National Science Fund for Distinguished Young Scholars and the State Council Special Allowance, he has been recognized as a leading talent in scientific and technological innovation under China’s "Ten Thousand Talents Plan." He has supervised numerous PhD and master’s students, including Xiang Ni, winner of the Zhong Jiaqing Outstanding Master’s Thesis Award from the Chinese Mathematical Society.
