Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory write by Lindsay Childs. This book was released on 2000. Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory available in PDF, EPUB and Kindle. 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.
Hopf Algebras and Galois Module Theory
Hopf Algebras and Galois Module Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hopf Algebras and Galois Module Theory write by Lindsay N. Childs. This book was released on 2021-11-10. Hopf Algebras and Galois Module Theory available in PDF, EPUB and Kindle. 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.
Advances in Hopf Algebras
Advances in Hopf Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Hopf Algebras write by Jeffrey Bergen. This book was released on 2023-08-18. Advances in Hopf Algebras available in PDF, EPUB and Kindle. "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. "
Galois Theory, Hopf Algebras, and Semiabelian Categories
Galois Theory, Hopf Algebras, and Semiabelian Categories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Galois Theory, Hopf Algebras, and Semiabelian Categories write by George Janelidze, Bodo Pareigis, and Walter Tholen. This book was released on . Galois Theory, Hopf Algebras, and Semiabelian Categories available in PDF, EPUB and Kindle.
Fundamentals of Hopf Algebras
Fundamentals of Hopf Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fundamentals of Hopf Algebras write by Robert G. Underwood. This book was released on 2015-06-10. Fundamentals of Hopf Algebras available in PDF, EPUB and Kindle. 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.
