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Author: Serge Bouc
Publisher: American Mathematical Soc.
ISBN: 0821819518
Category : Mathematics
Languages : en
Pages : 89
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Book Description
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: Serge Bouc
Publisher: American Mathematical Soc.
ISBN: 0821819518
Category : Mathematics
Languages : en
Pages : 89
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Book Description
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: serge Bouc
Publisher: Springer
ISBN: 3642112978
Category : Mathematics
Languages : en
Pages : 303
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Book Description
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: M. Hazewinkel
Publisher: Elsevier
ISBN: 9780080532967
Category : Mathematics
Languages : en
Pages : 896
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Book Description
Handbook of Algebra
Author: Alexander Fel'shtyn
Publisher: American Mathematical Soc.
ISBN: 0821820907
Category : Mathematics
Languages : en
Pages : 165
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Book Description
In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
Author: Michael Grosser
Publisher: American Mathematical Soc.
ISBN: 0821827294
Category : Mathematics
Languages : en
Pages : 113
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Book Description
In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.
Author: Palle E. T. Jørgensen
Publisher: American Mathematical Soc.
ISBN: 0821826883
Category : Mathematics
Languages : en
Pages : 74
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Book Description
Let $N\in\mathbb{N}$, $N\geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{\ast}$-algebra $\mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU DEGREES{-1}=V DEGREES{N}$. The representations are in one-to-one correspondence with solutions $h\in L DEGREES{1}\left(\mathbb{T}\right)$, $h\geq0$, to $R\left(h\right)=h$ where $R$ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $\mathfrak{A}_{N}$ may also be viewed as representations of a certain (discrete) $N$-adic $ax+b$ group which was considered recently
Author: Yasuro Gon
Publisher: American Mathematical Soc.
ISBN: 0821827634
Category : Mathematics
Languages : en
Pages : 130
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Book Description
Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
Author: M. van den Bergh
Publisher: American Mathematical Soc.
ISBN: 0821827545
Category : Mathematics
Languages : en
Pages : 157
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Book Description
This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.
Author: Paul Selick
Publisher: American Mathematical Soc.
ISBN: 0821821105
Category : Mathematics
Languages : en
Pages : 122
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Book Description
This book is intended for graduate students and research mathematicians interested in topology and representation theory.
Author: Lisa Carbone
Publisher: American Mathematical Soc.
ISBN: 0821827219
Category : Mathematics
Languages : en
Pages : 146
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Book Description
This title provides a comprehensive examination of non-uniform lattices on uniform trees. Topics include graphs of groups, tree actions and edge-indexed graphs; $Aut(x)$ and its discrete subgroups; existence of tree lattices; non-uniform coverings of indexed graphs with an arithmetic bridge; non-uniform coverings of indexed graphs with a separating edge; non-uniform coverings of indexed graphs with a ramified loop; eliminating multiple edges; existence of arithmetic bridges. This book is intended for graduate students and research mathematicians interested in group theory and generalizations.
