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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 TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHirosaki 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
Keywordstensor 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.

  • Research Products

    (4 results)

All Other

All Publications (4 results)

  • [Publications] D.Tambara: "Invariants and semi-direct products for finite group actions on tensor categories"J. Math. Soc. Japan. 53. 429-456 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D.Tambara: "A duality for modules over monoidal categories of representations of semi-simple Hopf Hopf algebras"Journal of Algebra. 241. 515-547 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D. Tambara: "Invariants and semi-direct products for finite group actions on tensor categories"J. Math. Soc. Japan. vol. 53. 429-456 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D. Tambara: "A duality for modules over monoidal categories of representations of semi-simple Hopt algebras"J. Algebra. vol. 241. 515-547 (2001)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2003-09-17  

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