Electronic ISBN:  9781470402747 
Product Code:  MEMO/144/683.E 
74 pp 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $30.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 144; 2000MSC: 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 nonadditive 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.ReadershipGraduate 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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First I will introduce a generalization of the notion of (right)exact functor between abelian categories to the case of nonadditive 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.
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