2001 Fiscal Year Final Research Report Summary
Study of monoidal categories
| Project/Area Number |
12640003
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hirosaki University |
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Principal Investigator |
TAMBARA Daisuke Faculty of Science and Technology, Hirosaki University, Assistant Professor, 理工学部, 助教授 (50163712)
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| Project Period (FY) |
2000 – 2001
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| Keywords | tensor category / Mackey category |
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| 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.
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