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Author: Lindsay N. Childs
Publisher: American Mathematical Soc.
ISBN: 1470465167
Category : Education
Languages : en
Pages : 311
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Book Description
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.
Author: Lindsay N. Childs
Publisher: American Mathematical Soc.
ISBN: 1470465167
Category : Education
Languages : en
Pages : 311
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Book Description
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.
Author: Robert G. Underwood
Publisher: Springer Science & Business Media
ISBN: 0387727655
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Only book on Hopf algebras aimed at advanced undergraduates
Author: Lindsay Childs
Publisher: American Mathematical Soc.
ISBN: 0821821318
Category : Mathematics
Languages : en
Pages : 225
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Book Description
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.
Author: Stephen U. Chase
Publisher: Springer
ISBN: 3540361340
Category : Mathematics
Languages : en
Pages : 139
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Book Description
Author: Sorin Dascalescu
Publisher: CRC Press
ISBN: 1482270749
Category : Mathematics
Languages : en
Pages : 420
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Book Description
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.
Author: Daniel Bulacu
Publisher: Cambridge University Press
ISBN: 1108427014
Category : Mathematics
Languages : en
Pages : 545
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Book Description
This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
Author: Moss E. Sweedler
Publisher:
ISBN:
Category : Hopf algebras
Languages : en
Pages : 360
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Book Description
Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 0429530072
Category : Mathematics
Languages : en
Pages : 348
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Book Description
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the
Author: Pavel Etingof
Publisher: American Mathematical Soc.
ISBN: 1470434415
Category : Mathematics
Languages : en
Pages : 362
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Book Description
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Author: George Janelidze, Bodo Pareigis, and Walter Tholen
Publisher: American Mathematical Soc.
ISBN: 9780821871478
Category :
Languages : en
Pages : 588
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Book Description
