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Advances In Hopf Algebras
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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 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 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
Book Synopsis Classical Hopf Algebras and Their Applications by : Pierre Cartier
Download or read book Classical Hopf Algebras and Their Applications written by Pierre Cartier and published by Springer Nature. This book was released on 2021-09-20 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.
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: Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.
Book Synopsis Hopf Algebras and Root Systems by : István Heckenberger
Download or read book Hopf Algebras and Root Systems written by István Heckenberger and published by American Mathematical Soc.. This book was released on 2020-06-19 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras for advanced graduate students and researchers working in categorial aspects and classification theory of Hopf algebras and their generalization.
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 2023-08-18 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. "
Download or read book Hopf Algebras written by David E. Radford and published by World Scientific. This book was released on 2012 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.
Book Synopsis Tensor Categories by : Pavel Etingof
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Hopf Algebras in Noncommutative Geometry and Physics by : Stefaan Caenepeel
Download or read book Hopf Algebras in Noncommutative Geometry and Physics written by Stefaan Caenepeel and published by CRC Press. This book was released on 2019-05-07 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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.
Download or read book Hopf Algebras written by Jeffrey Bergen and published by CRC Press. This book was released on 2004-01-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume publishes key proceedings from the recent International Conference on Hopf Algebras held at DePaul University, Chicago, Illinois. With contributions from leading researchers in the field, this collection deals with current topics ranging from categories of infinitesimal Hopf modules and bimodules to the construction of a Hopf algebraic
Book Synopsis Algebras, Rings and Modules by : Michiel Hazewinkel
Download or read book Algebras, Rings and Modules written by Michiel Hazewinkel and published by CRC Press. This book was released on 2016-04-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.
Book Synopsis Rings, Hopf Algebras, and Brauer Groups by : Stefaan Caenepeel
Download or read book Rings, Hopf Algebras, and Brauer Groups written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-09-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "
Download or read book Hopf Algebras written by David E Radford and published by World Scientific. This book was released on 2011-12-28 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph. Contents:PreliminariesCoalgebrasRepresentations of CoalgebrasThe Coradical Filtration and Related StructuresBialgebrasThe Convolution AlgebraHopf AlgebrasHopf Modules and Co-Hopf ModulesHopf Algebras as Modules Over Their Hopf SubalgebrasIntegralsActions by Bialgebras and Hopf AlgebrasQuasitriangular Bialgebras and Hopf AlgebrasThe Drinfel'd Double of a Finite-Dimensional Hopf AlgebraCo-Quasitriangular Bialgebras and Hopf AlgebrasPointed Hopf AlgebrasFinite-Dimensional Hopf Algebras in Characteristic 0 Readership: Undergraduates and researchers in algebra and number theory. Keywords:Hopf Algebras;Coalgebras;Quantum GroupsKey Features:Provides a good foundation for those who wish to study Hopf algebras on their ownProvides a firm foundation for those who are more interested in applications to other areasGives many exercises which suggest connections to exploreReviews: "With this monograph, one of the pioneers of the subject provides a comprehensive introduction to the theory of Hopf algebras. As this theory has made great strides in recent years, such a monograph constitutes a very valuable addition to the literature, especially as there are so far comparatively few textbooks on this topic. Radford's book contains at the end of each chapter a very useful set of chapter notes that discuss these references and therefore provide an entry point to the recent research literature, especially to the extensive literature on the classification of finite–dimensional pointed Hopf algebras, a topic not discussed in any of the other books. For all these reasons, Radford's book is a very valuable new textbook on Hopf algebras that will be frequently used both by students and by researchers." Mathematical Reviews "A big number of exercises of different level of difficulty are proposed along the text, which include in particular special features or applications to a variety of concrete examples, further results and categorical aspects of the corresponding material. Interesting and up-to-date historical and bibliographical comments are provided at the end of each of the sixteen chapters." Zentralblatt MATH
Book Synopsis Quasi-Hopf Algebras by : Daniel Bulacu
Download or read book Quasi-Hopf Algebras written by Daniel Bulacu and published by Cambridge University Press. This book was released on 2019-02-21 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
