Abstract
This talk is about the Rota-Baxter operators on Hopf algebras and Hopf modules. On the basis of Rota-Baxter operators on groups given by Guo et al, we and Goncharov introduce the concepts of Rota-Baxter Hopf algebras and Rota-Baxter weak Hopf algebras, respectively, and prove that Rota-Baxter operators on the commutative Hopf algebra H (H = k[G] the group algebra of a group G or H = U(g) the universal enveloping algebra of a Lie algebra g) are in one to one correspondence with corresponding Rota-Baxter operators on groups or Lie algebras, and construct Rota-Baxter operators from the normalized integral, antipode, and target map of a given commutative weak Hopf algebra. We also obtain some characterizations of Rota-Baxter paired modules, and obtain a large number of Rota-Baxter paired modules from Hopf related algebras and modules, including semisimple Hopf algebras, dimodules and weak Doi-Hopf modules. Some of them give new examples of Rota-Baxter algebras. We also introduce the concept of Rota-Baxter paired Hopf modules by combining the notion of Rota-Baxter paired module with Rota-Baxter paired comodule, and prove a structure theorem for generic Rota-Baxter paired Hopf modules.
About the Speaker
张良云，教授、博士生导师。江苏省“333高层次人才培养工程”首批中青年科学技术带头人，南京农业大学第一届和第二届“133青年教师优秀学术带头人”。现担任江苏省高等学校数学教学研究会副理事长，南京农业大学数学一级学科点点长。先后主持国家自然科学面上基金、教育部科学技术重点基金、高等学校博士学科点专项基金、江苏省自然科学基金和中国博士后科研基金等科研项目，以及主编国家级“十五”和“十一五”规划教材《线性代数》，以及主编农业部“十二五”和“十三五”规划教材《高等数学》等。先后获得江苏省教学成果奖、江苏省精品教材奖、江苏省重点教材奖、南京农业大学优秀教师奖和教学质量优秀奖等，并在Journal of Algebra、 Journal of Pure and Applied Algebra和Algebras and Representation Theory等代数学核心杂志上发表100多篇学术论文。