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Non-Additive Exact Functors and Tensor Induction for Mackey Functors
 
Serge Bouc Université Paris, Paris, France
Front Cover for Non-Additive Exact Functors and Tensor Induction for Mackey Functors
Available Formats:
Electronic ISBN: 978-1-4704-0274-7
Product Code: MEMO/144/683.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $30.00
Front Cover for Non-Additive Exact Functors and Tensor Induction for Mackey Functors
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  • Front Cover for Non-Additive Exact Functors and Tensor Induction for Mackey Functors
  • Back Cover for Non-Additive Exact Functors and Tensor Induction for Mackey Functors
Non-Additive Exact Functors and Tensor Induction for Mackey Functors
Serge Bouc Université Paris, Paris, France
Available Formats:
Electronic ISBN:  978-1-4704-0274-7
Product Code:  MEMO/144/683.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $30.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1442000; 74 pp
    MSC: Primary 18; 19; Secondary 20;

    First I will introduce a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category.

    Next I use those results to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for \(p\)-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.

    Readership

    Graduate students and research mathematicians interested in representation theory of finite groups.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Non additive exact functors
    • 3. Permutation Mackey functors
    • 4. Tensor induction for Mackey functors
    • 5. Relations with the functors $\mathcal {L}_U$
    • 6. Direct product of Mackey functors
    • 7. Tensor induction for Green functors
    • 8. Cohomological tensor induction
    • 9. Tensor induction for $p$-permutation modules
    • 10. Tensor induction for modules
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Volume: 1442000; 74 pp
MSC: Primary 18; 19; Secondary 20;

First I will introduce a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category.

Next I use those results to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for \(p\)-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.

Readership

Graduate students and research mathematicians interested in representation theory of finite groups.

  • Chapters
  • 1. Introduction
  • 2. Non additive exact functors
  • 3. Permutation Mackey functors
  • 4. Tensor induction for Mackey functors
  • 5. Relations with the functors $\mathcal {L}_U$
  • 6. Direct product of Mackey functors
  • 7. Tensor induction for Green functors
  • 8. Cohomological tensor induction
  • 9. Tensor induction for $p$-permutation modules
  • 10. Tensor induction for modules
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