报告人简介
李立斌：扬州大学数学科学学院副院长、教授、博士生导师。近年来，先后应邀到德国Bielefeld大学、Oxford大学、筑波大学、悉尼大学等大学和研究所进行学术交流。主持和参与多项国家自然科学基金项目。在《Journal of Agebras》、《Contemp. Math》、《Alg. Rep.Theory》等国内外刊物上发表论文50余篇。研究兴趣: Hopf代数与量子群的表示理论、李理论与张量范畴。

摘要: Casimir number is an important invariant of a _nite tensor
category. Let C be a _nite tensor category with _nitely many isomor-
phism classes of indecomposable objects over an algebraically closed field k. The _rst part of this talk is concerned with the question when the
Green ring G(C), or the Green algebra G(C) Z K over a _eld K, is Ja-
cobson semisimple. It turns out that G(C)Z K is Jacobson semisimple
if and only if the Casimir number of C is not zero in K. For the Green
ring G(C) itself, G(C) is Jacobson semisimple if and only if the Casimir
number of C is not zero. In the second part we shall focus on the case
where C = Rep(kG) for a cyclic group G of order p over a field k of
characteristic p. In this case, the Casimir number of C is computable
and is shown to be 2p^2. This leads to a complete description of the
Jacobson radical of the Green algebra G(C) Z K over any field K.