University of Sydney Algebra Seminar

Prof. Fang Li (Zhejiang University)

Friday 27 February, 12:05-12:55pm, Place: 359

On representations rings in the context of monoidal categories

The broad aim of this work is to develop a unified framework for investigating representations of Hopf algebras through the study of Green rings of various categories related to them. We introduce the notion of Green rings of monoidal categories, then examine the relationship among the Green rings of some examples of monoidal categories such as module categories, complex categories, homotopy categories, derived categories and (derived) shift categories. The more concrete part of this talk is to characterize representation rings and derived rings of a class of Hopf algebras A_n=KZ_n/J^d, which are constructed from Nakayama truncated algebras. We determine the generators and defining relations of each representation ring r(A_n); we also give a presentation for each derived ring dr(A_n) (i.e., d=2). Polynomial characterizations of these (derived) representation rings are discussed.