| 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.
|
