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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 Click above image for expanded view 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.

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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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.

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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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