2016年度威廉希尔外请专家学术报告之二十六

时间：2016-10-12 09:19:37 来源： 作者：数学学院

报告题目： On representation rings in the context of monoidal categories

报 告 人：李方教授

报告时间：2016年10月24日（周一）上午9:00―10:00

报告地点：威廉希尔学术报告厅

报告摘要：In general, representation rings are well-known as Green rings from module categories of Hopf algebras.In this paper, we study Green rings in the context of monoidal categories such that representations of Hopf algebras can be investigated through Green rings of various levels from module categories to derived categories in the unified view-point. Firstly, as analogue of representation rings of Hopf algebras, we set up the
so-called Green rings of monoidal categories, and then list some such categories including module categories, complex categories, homotopy categories, derived categories and (derived) shift categories, etc. and the relationship among their corresponding Green rings. The main part of this paper is to characterize representation rings and derived rings of a class of Hopf algebras constructed from Nakayama truncated algebras, denoted concretely as $KZ_n/J^d$. For the representation ring $r(KZ_n/J^d)$, we completely determine its generators and the relations of generators via the method of Pascal triangle. For the derived ring $dr(KZ_n/J^2)$(i.e., $d=2$), we determine its generators and give the relations of generators. In these two aspects, the polynomial characterizations of the representation ring and the derived ring are both given.

报告人简介：李方，浙江大学数学科学学院教授，博士生导师。1991年获兰州大学博士学位，1993年兰州大学理论物理方向博士后出站。曾在兰州大学、东南大学、杭州大学工作。1998年入选浙江省151人才工程培养对象，2004年入选教育部“新世纪优秀人才支持计划”。先后多次到香港城市大学、澳大利亚Tasmania大学、西澳大利亚大学、悉尼大学、Queensland大学、New South Wiles大学、德国Bielefeld大学、慕尼黑大学、英国Warwick大学等进行学术访问。德国Zentralblatt fur Math.、美国Math.Reviews评论员。主要从事代数表示论，Hopf代数和量子群，环与代数，群和半群表示理论等领域的研究工作。

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威廉希尔

2016年10月11日