Biset Functors For Finite Groups
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| Author | : serge Bouc |
| Publisher | : Springer |
| Total Pages | : 303 |
| Release | : 2010-03-10 |
| Genre | : Mathematics |
| ISBN | : 3642112978 |
This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics on biset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted to biset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors to long-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting of advanced results in the area, with some new ideas and proofs.
| Author | : Scott Balchin |
| Publisher | : Cambridge University Press |
| Total Pages | : 357 |
| Release | : 2021-11-18 |
| Genre | : Mathematics |
| ISBN | : 1108931944 |
A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.
| Author | : Stefan Schwede |
| Publisher | : Cambridge University Press |
| Total Pages | : 847 |
| Release | : 2018-09-06 |
| Genre | : Mathematics |
| ISBN | : 110842581X |
A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
| Author | : Petter Andreas Bergh |
| Publisher | : Springer Nature |
| Total Pages | : 275 |
| Release | : |
| Genre | : |
| ISBN | : 3031577892 |
| Author | : Robert Adler |
| Publisher | : Springer |
| Total Pages | : 135 |
| Release | : 2011-05-16 |
| Genre | : Mathematics |
| ISBN | : 3642195806 |
These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
| Author | : Jan Lang |
| Publisher | : Springer |
| Total Pages | : 232 |
| Release | : 2011-03-17 |
| Genre | : Mathematics |
| ISBN | : 3642184294 |
The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.
| Author | : Jan Šťovíček |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 298 |
| Release | : 2020-11-13 |
| Genre | : Education |
| ISBN | : 147045131X |
This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.
| Author | : Nadia Mazza |
| Publisher | : Springer |
| Total Pages | : 127 |
| Release | : 2019-05-25 |
| Genre | : Mathematics |
| ISBN | : 3030181561 |
This is an in-depth report on the endotrivial modules, an important class of modular representations for finite groups. Following the historical development of the theory, the book starts with a review of the necessary definitions and some key examples. The main results obtained using traditional techniques are then presented, followed by more recent results such as the work of Grodal inspired by algebraic topology. In the last part of the book original methods are applied to obtain the group of endotrivial modules for certain very important groups. An accessible reference collecting half a century of research on endotrivial modules, this book will be of interest to researchers in algebra.
| Author | : Serge Bouc |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 89 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821819518 |
First the author introduces 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 those results are used 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.
| Author | : Thomas Duquesne |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 216 |
| Release | : 2010-09-05 |
| Genre | : Mathematics |
| ISBN | : 3642140068 |
Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.
