A Criterion for the semi-simplicity of the representation algebra of a finite tensor category

主 讲 人 ：李立斌    教授

活动时间：07月30日10时00分    

地      点 ：数信学院D-204室

讲座内容：

This talk deals with the representation algebra of afinite tensor category  with finitely many isomorphism classes ofindecomposable objects over an algebraically closed field F. The first part ofthis talk is concerned with the question when the representation ring and therepresentation algebra over a field K is Jacobson semi-simple (namely, has zeroJacobson radical). It turns out that the representation algebra is Jacobsonsemi-simple if and only if the Casimir number of the tensor category is notzero in K. For the representation ring being Jacobson semi-simple if and onlyif the Casimir number of the tensor category is not zero. In the second part weshall focus on the case where the tensor category is the representationcategory over a cyclic group algebra with order prime number p over a fieldwith characteristic p. In this case, the Casimir number is computable . Thisleads to a complete description of the Jacobson radical of the representationalgebra.

主讲人介绍：

李立斌，扬州大学数学科学学院博士生导师、教授，2000年在中国科学技术大学取得博士学位。近几年来，先后应邀到德国比勒费尔德大学、亚琛工业大学、科隆大学、英国莱斯特大学、牛津大学、伦敦城市大学、华威大学、台湾大学、南洋理工大学、筑波大学、比利时哈瑟尔特等大学进行学术交流。先后主持三项国家自然科学基金、一项教育部博士点基金、一项省自然科学基金，在国内外重要期刊发表学术论文50余篇。

发布时间：2018-07-30 17:41:47