Modules And Comodules

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Modules And Comodules

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Author : Tomasz Brzezinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-26

Modules And Comodules written by Tomasz Brzezinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-26 with Mathematics categories.

The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and dedicated to Robert Wisbauer on the occasion of his 65th birthday. These articles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory, some of which have a long tradition whereas others have emerged in recent years. They include topics in the formal theory of modules bordering on category theory, in ring theory, in Hopf algebras and quantum groups, and in corings and comodules.

International Conference On Modules And Comodules 8 10 September 2006 University Of Porto

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Author : International Conference on Modules and Comodules
language : en
Publisher:
Release Date : 2006

International Conference On Modules And Comodules 8 10 September 2006 University Of Porto written by International Conference on Modules and Comodules and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Modules And Comodules Over Nonarchimedean Hopf Algebras

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Author : Anton Lyubinin
language : en
Publisher:
Release Date : 2010

Modules And Comodules Over Nonarchimedean Hopf Algebras written by Anton Lyubinin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

The purpose of this work is to study Hopf algebra analogs of constructions in the theory of p-adic representations of p-adic groups. We study Hopf algebras and comodules, whose underlying vector spaces are either Banach or compact inductive limits of such. This framework is unifying for the study of continuous and locally analytic representations of compact p-adic groups, affinoid and sigma-affinoid groups and their quantized analogs. We define the analog of Frechet-Stein structure for Hopf algebra (which play role of the function algebra), which we call CT-Stein structure. We prove that a compact type structure on a CT-Hopf algebra is CT-Stein if its dual is a nuclear Frechet-Stein structure on the dual NF-Hopf algebra. We show that for every compact p-adic group the algebra of locally analytic functions on that group is CT-Stein. We describe admissible representations in terms of comodules, which we call admissible comodules, and thus we prove that admissible locally analytic representations of compact p-adic groups are compact inductive limits of artinian locally analytic Banach space representations. We introduce quantized analogs of algebras Ur(sl2;K) from [7] thus giving an example of in fite-dimensional noncommutative and noncocommutative nonarchimedean Banach Hopf algebra. We prove that these algebras are Noetherian. We also introduce a quantum analog of U(sl2;K) and we prove that it is a (in fite-dimensional non-commutative and non-cocommutative) Frechet-Stein Hopf algebra. We study the cohomology theory of nonarchimedean comodules. In the case of modules and algebras this was done by Kohlhasse, following the framework of J.L. Taylor. We use an analog of the topological derived functor of Helemskii to develop a cohomology theory of non-archimedean comodules (this approach can be applied to modules too). The derived functor approach allows us to discuss a Grothendieck spectral sequence (GSS) in our context. We apply GSS theorem to prove generalized tensor identity and give an example, when this identity is nontrivial.

Revue Roumaine De Math Matiques Pures Et Appliqu Es

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Author :
language : en
Publisher:
Release Date : 2007

Revue Roumaine De Math Matiques Pures Et Appliqu Es written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Coprime Modules And Comodules

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Author : Indah Emilia Wijayanti
language : en
Publisher:
Release Date : 2005

Coprime Modules And Comodules written by Indah Emilia Wijayanti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

American Journal Of Mathematics

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Author :
language : en
Publisher:
Release Date : 2003

American Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.

Rational Representations The Steenrod Algebra And Functor Homology

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Author : Vincent Franjou
language : en
Publisher:
Release Date : 2003

Rational Representations The Steenrod Algebra And Functor Homology written by Vincent Franjou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

The book presents aspects of homological algebra in functor categories, with emphasis on polynomial functors between vector spaces over a finite field. With these foundations in place, the book presents applications to representation theory, algebraic topology and $K$-theory. As these applications reveal, functor categories offer powerful computational techniques and theoretical insights. T. Pirashvili sets the stage with a discussion of foundations. E. Friedlander then presents applications to the rational representations of general linear groups. L. Schwartz emphasizes the relation of functor categories to the Steenrod algebra. Finally, V. Franjou and T. Pirashvili present A. Scorichenko's understanding of the stable $K$-theory of rings as functor homology. The book is suitable for graduate students and researchers interested in algebra and algebraic geometry.

Osaka Journal Of Mathematics

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Author :
language : en
Publisher:
Release Date : 1983

Osaka Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

On The Structure Of Hopf Algebras

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Author : John Willard Milnor
language : en
Publisher:
Release Date : 1962

On The Structure Of Hopf Algebras written by John Willard Milnor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Algebraic topology categories.

Corings And Comodules

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Author : Tomasz Brzezinski
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-15

Corings And Comodules written by Tomasz Brzezinski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Mathematics categories.

This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry.