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Hopf Algebras And Galois Module Theory
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Book Synopsis Hopf Algebras and Galois Module Theory by : Lindsay N. Childs
Download or read book Hopf Algebras and Galois Module Theory written by Lindsay N. Childs and published by American Mathematical Soc.. This book was released on 2021-11-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory by : Lindsay Childs
Download or read book Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory written by Lindsay Childs and published by American Mathematical Soc.. This book was released on 2000 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hopf Algebras and Galois Theory by : Stephen U. Chase
Download or read book Hopf Algebras and Galois Theory written by Stephen U. Chase and published by Springer. This book was released on 2007-01-05 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Hopf Algebras by : Robert G. Underwood
Download or read book An Introduction to Hopf Algebras written by Robert G. Underwood and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Only book on Hopf algebras aimed at advanced undergraduates
Author :George Janelidze, Bodo Pareigis, and Walter Tholen Publisher :American Mathematical Soc. ISBN 13 :9780821871478 Total Pages :588 pages Book Rating :4.8/5 (714 download)
Book Synopsis Galois Theory, Hopf Algebras, and Semiabelian Categories by : George Janelidze, Bodo Pareigis, and Walter Tholen
Download or read book Galois Theory, Hopf Algebras, and Semiabelian Categories written by George Janelidze, Bodo Pareigis, and Walter Tholen and published by American Mathematical Soc.. This book was released on with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Brauer Groups, Hopf Algebras and Galois Theory by : Stefaan Caenepeel
Download or read book Brauer Groups, Hopf Algebras and Galois Theory written by Stefaan Caenepeel and published by Springer Science & Business Media. This book was released on 2002-03-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Galois Theory, Hopf Algebras, and Semiabelian Categories by : George Janelidze
Download or read book Galois Theory, Hopf Algebras, and Semiabelian Categories written by George Janelidze and published by American Mathematical Soc.. This book was released on 2004 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advances in Hopf Algebras by : Jeffrey Bergen
Download or read book Advances in Hopf Algebras written by Jeffrey Bergen and published by CRC Press. This book was released on 1994-04-19 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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. "
Book Synopsis An Introduction to Hopf Algebras by : Robert G. Underwood
Download or read book An Introduction to Hopf Algebras written by Robert G. Underwood and published by Springer. This book was released on 2011-08-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Only book on Hopf algebras aimed at advanced undergraduates
Book Synopsis Hopf Algebras and Galois Theory by : Stephen U. Chase
Download or read book Hopf Algebras and Galois Theory written by Stephen U. Chase and published by . This book was released on 2014-01-15 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of Hopf Algebras by : Robert G. Underwood
Download or read book Fundamentals of Hopf Algebras written by Robert G. Underwood and published by Springer. This book was released on 2015-06-10 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course. Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields and linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforward applications of the theory to problems that are devised to challenge the reader. Questions for further study are provided after selected exercises. Most proofs are given in detail, though a few proofs are omitted since they are beyond the scope of this book.
Book Synopsis Hopf Algebras and Their Actions on Rings by : Susan Montgomery
Download or read book Hopf Algebras and Their Actions on Rings written by Susan Montgomery and published by American Mathematical Soc.. This book was released on 1993-10-28 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.
Book Synopsis Hopf Algebras and Galois Theory Two by : U. Chase
Download or read book Hopf Algebras and Galois Theory Two written by U. Chase and published by . This book was released on 1969-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebras, Rings and Modules by : Michiel Hazewinkel
Download or read book Algebras, Rings and Modules written by Michiel Hazewinkel and published by American Mathematical Soc.. This book was released on 2010 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.
Download or read book Hopf Algebra written by Sorin Dascalescu and published by CRC Press. This book was released on 2000-09-15 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study covers comodules, rational modules and bicomodules; cosemisimple, semiperfect and co-Frobenius algebras; bialgebras and Hopf algebras; actions and coactions of Hopf algebras on algebras; finite dimensional Hopf algebras, with the Nicholas-Zoeller and Taft-Wilson theorems and character theory; and more.
Book Synopsis New Directions in Hopf Algebras by : Susan Montgomery
Download or read book New Directions in Hopf Algebras written by Susan Montgomery and published by Cambridge University Press. This book was released on 2002-05-06 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains survey articles for graduate students and researchers on various topics surrounding Hopf algebras.
Download or read book Hopf Algebra written by Sorin Dascalescu and published by CRC Press. This book was released on 2000-09-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study covers comodules, rational modules and bicomodules; cosemisimple, semiperfect and co-Frobenius algebras; bialgebras and Hopf algebras; actions and coactions of Hopf algebras on algebras; finite dimensional Hopf algebras, with the Nicholas-Zoeller and Taft-Wilson theorems and character theory; and more.
