Hopf Algebras And Galois Theory
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Hopf Algebras And Galois Module Theory
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Author : Lindsay N. Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-10
Hopf Algebras And Galois Module Theory written by Lindsay N. Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Education categories.
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Hopf Algebras And Galois Theory
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Author : Stephen U. Chase
language : en
Publisher: Springer
Release Date : 2007-01-05
Hopf Algebras And Galois Theory written by Stephen U. Chase and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.
Brauer Groups Hopf Algebras And Galois Theory
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Author : Stefaan Caenepeel
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-03-31
Brauer Groups Hopf Algebras And Galois Theory written by Stefaan Caenepeel 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 2002-03-31 with Mathematics categories.
This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.
Hopf Algebras And Galois Theory
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Author : Stephen U. Chase
language : en
Publisher:
Release Date : 2014-01-15
Hopf Algebras And Galois Theory written by Stephen U. Chase and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Hopf Algebras And Galois Theory Two
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Author : U. Chase
language : en
Publisher:
Release Date : 1969-05
Hopf Algebras And Galois Theory Two written by U. Chase and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969-05 with categories.
Galois Theory Hopf Algebras And Semiabelian Categories
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Author : George Janelidze
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Galois Theory Hopf Algebras And Semiabelian Categories written by George Janelidze and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume is based on talks given at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories held at The Fields Institute for Research in Mathematical Sciences (Toronto, ON, Canada). The meeting brought together researchers working in these interrelated areas. This collection of survey and research papers gives an up-to-date account of the many current connections among Galois theories, Hopf algebras, and semiabeliancategories. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higher-dimensional structures. Articles are suitable for graduate students and researchers,specifically those interested in Galois theory and Hopf algebras and their categorical unification.
Taming Wild Extensions Hopf Algebras And Local Galois Module Theory
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Author : Lindsay Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Taming Wild Extensions Hopf Algebras And Local Galois Module Theory written by Lindsay Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory. Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree p and p2; and Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.
Galois Theory Hopf Algebras And Semiabelian Categories
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Author : George Janelidze, Bodo Pareigis, and Walter Tholen
language : en
Publisher: American Mathematical Soc.
Release Date :
Galois Theory Hopf Algebras And Semiabelian Categories written by George Janelidze, Bodo Pareigis, and Walter Tholen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Advances In Hopf Algebras
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Author : Jeffrey Bergen
language : en
Publisher: CRC Press
Release Date : 1994-04-19
Advances In Hopf Algebras written by Jeffrey Bergen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-19 with Mathematics categories.
"This remarkable reference covers topics such as quantum groups, Hopf Galois theory, actions and coactions of Hopf algebras, smash and crossed products, and the structure of cosemisimple Hopf algebras. "
Brauer Groups Hopf Algebras And Galois Theory
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Author : Stefaan Caenepeel
language : en
Publisher: Springer
Release Date : 2002-04-14
Brauer Groups Hopf Algebras And Galois Theory written by Stefaan Caenepeel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-14 with Mathematics categories.
This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.