2001 Fiscal Year Final Research Report Summary

Study of monoidal categories

Research Project

Project/Area Number	12640003
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Hirosaki University
Principal Investigator	TAMBARA Daisuke Faculty of Science and Technology, Hirosaki University, Assistant Professor, 理工学部, 助教授 (50163712)
Project Period (FY)	2000 – 2001
Keywords	tensor category / Mackey category
Research Abstract	Let A be a tensor category. We define the category D(A) as follows. An object of D(A) consists of the following data: vector spaces F(X,Y) for all objects X and Y ofA, linear maps F(X,Y)-->F(X',Y') for all morphisms X'-->X and Y->Y' of A, and linear maps F(X,Y) -->F(ZX,ZY) and F(X,Y) -->F(XZ,YZ) for all objects X, Y, and Z of A. These data should satisfy certain conditions. Here we denote by ZX the tensorproduct of Z and X in A. When A is semi-simple, the category D(A) is equivalent to the center of A. As an interesting example of non semi-simple tensor categories, we take A to be the Mackey category M of a finite group G. Then D(M) turns out to be equivalent to the category of a kind of Mackey functors over the category of connected G-sets equipped with automorphisms.

(4 results)