学术报告一

报告人：张印火教授 （比利时Hasselt大学）

报告题目：On Green rings of finite-dimensional Hopf algebras

报告时间：9月7号上午9:50-10:40

报告地点：25教18楼1802

参加人员：教师、研究生、本科生

报告摘要：We study the Green ring and the stable Green ring of a finite dimensional Hopf algebra by means of bllinear forms. We show that the Green ring of a Hopf algebra of finite representation type is a Frobenius algebra over Z with a dual basis associated to almost split sequences. On the stable Green ring we define a new bilinear form which is more accurate to determine the bi-Frobenius algebra structure on the stable Green ring. We show that the complexified stable Green algebra is a group-like algebra, and hence a bi-Frobenius algebra, if the bilinear form on the stable Green ring is non-degenerate.

报告人简介：张印火：Hopf代数和张量范畴理论国际知名专家, 在Hopf代数的Green 环和Brauer 群方面做了许多开创性和深刻的工作。于1991年在比利时获得博士学位，后在新西兰和比利时任教授。在 《Trans. Amer. Math. Soc.》， 《J. Noncommut. Geom.》， 《Math. Z.》， 《Israel J. Math.》， 《J. Algebra 》等高水平杂志发表论文70多篇，被同行引用600余次。现为比利时Hasselt大学终身教授，是每一年一次的Hopf代数与Tensor Categories国际会议的发起人和组织者。

学术报告二

报告人：李立斌教授 （扬州大学）

报告题目：Maschke’s theorem of the Green algebra over a finite rigid tensor category

报告时间：9月7号上午10:50-11:40

报告地点：25教18楼1802

参加人员：教师、研究生、本科生

报告摘要：In this talk, we deal with the Casimir number of a rigid tensor category with finitely many isomorphism classes of indecomposable objects over an algebraically closed field K. The first part of this talk is concerned with the question when the Green ring is Jacobson semisimple. It turns out that the Green algebra is Jacobson semisimple if and only if the Casimir number is not zero. In the second part we shall focus on the case where the tensor category is the representation category of a cyclic group G with order P over a field K with charK=P. In this case, the Casimir number is computable. This leads to a complete description of the Jacoboson radical of the Green algebra.

报告人简介：李立斌：扬州大学教授，数学科学学院副经理。 主要从事Hopf代数，代数表示论，张量范畴等方面的研究。在《Journal of Algebra》，《Alg. Rep.Theory》，《Archiv der Mathematik》等国内外刊物上发表论文60余篇.主持国家自然科学基金面上项目4项。