报告人：张毅 副教授
报告题目：A monoidal categorical approach to augmented Rota-Baxter algebras and free cocycle bialgebras
报告时间：2026年7月11日（周六）下午4：00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
张毅，博士，副教授，硕士生导师，美国数学评论评论员，德国数学文摘评论员。主要从事代数表示论，Rota-Baxter代数与Hopf代数的研究，在Adv. Theor. Math. Phys.，Science China Math.，J. Algebra，JPAA，Pacific J. Math., J. Algebraic Combin.等国内外三高期刊发表SCI论文20余篇。现主持完成国家自然基金青年基金、科技部“一带一路”创新人才交流外国专家项目各1项。研究成果被美国数学物理学家，加州理工学院Marcolli教授，以及语言学家，美国国家科学院Chomsky院士应用到生成语言学中的Minimalist纲领。
报告摘要：
The ordinary tensor product of Rota-Baxter operators is not stable and therefore does not provide a natural monoidal structure on the category of Rota-Baxter algebras. We resolve this obstruction by passing to augmented Rota-Baxter algebras and by introducing a triangular tensor product governed by the augmentation. This construction makes the category of augmented Rota-Baxter algebras into a monoidal category. We identify its comonoid objects with Rota-Baxter cocycle bialgebras, thereby giving a categorical explanation for the Hochschild 1-cocycle condition. As an application, we construct a canonical bialgebra structure on the free commutative Rota-Baxter algebra generated by a commutative bialgebra, prove its universal property as a free commutative Rota-Baxter cocycle bialgebra, and obtain a Hopf algebra in the connected filtered case.