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.
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 282 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 Morita invariant. It uses the newly introduced theory of bi-Frobenius algebras to investigate a notion of group-like algebras and summarizes results on the classification of Hopf algebras of dimension pq. It also explores pre-Lie, dendriform, and Nichols algebras and discusses support cones for infinitesimal group schemes.
Download or read book New Directions and Applications in Control Theory written by Wijesuriya P. Dayawansa and published by Springer Science & Business Media. This book was released on 2005-08-31 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers in control theory and applications presented at a conference in honor of Clyde Martin on the occasion of his 60th birthday, held in Lubbock, Texas, November 14-15, 2003.
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.
Download or read book Hopf Algebras and Generalizations written by Louis H. Kauffman and published by American Mathematical Soc.. This book was released on 2007 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, motivations and applications throughout algebra, category theory, topology, geometry, quantum field theory, quantum gravity, and also combinatorics, logic, and theoretical computer science. This volume portrays the vitality of contemporary research in Hopf algebras. Altogether, the articles in the volume explore essential aspects of Hopf algebras and some of their best-known generalizations by means of a variety of approaches and perspectives. They make use of quite different techniques that are already consolidated in the area of quantum algebra. This volume demonstrates the diversity and richness of its subject. Most of its papers introduce the reader to their respective contexts and structures through very expository preliminary sections.
Download or read book Hopf Algebras Tensor Categories and Related Topics written by Nicolás Andruskiewitsch and published by American Mathematical Soc.. This book was released on 2021-07-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary topics discussed in the text include the classification of Hopf algebras, structures and actions of Hopf algebras, algebraic supergroups, representations of quantum groups, quasi-quantum groups, algebras in tensor categories, and the construction method of fusion categories.
Download or read book New Developments in Lie Theory and Its Applications written by Carina Boyallian and published by American Mathematical Soc.. This book was released on 2011 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on representation theory, harmonic analysis in Lie groups, and mathematical physics related to Lie theory. The papers give a broad overview of these subjects and also of the recent developments in research.
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 Algebras and Their Generalizations from a Category Theoretical Point of View written by Gabriella Böhm and published by Springer. This book was released on 2018-11-01 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications. Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras. Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.
Download or read book Tensor Categories and Hopf Algebras written by Nicolás Andruskiewitsch and published by American Mathematical Soc.. This book was released on 2019-04-18 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This volume contains the proceedings of the scientific session “Hopf Algebras and Tensor Categories”, held from July 27–28, 2017, at the Mathematical Congress of the Americas in Montreal, Canada. Papers highlight the latest advances and research directions in the theory of tensor categories and Hopf algebras. Primary topics include classification and structure theory of tensor categories and Hopf algebras, Gelfand-Kirillov dimension theory for Nichols algebras, module categories and weak Hopf algebras, Hopf Galois extensions, graded simple algebras, and bialgebra coverings.
Download or read book New Developments in Lie Theory and Geometry written by Carolyn Gordon and published by American Mathematical Soc.. This book was released on 2009 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.
Download or read book Handbook of Algebra written by and published by Elsevier. This book was released on 2003-10-15 with total page 1185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra
Download or read book Handbook of Algebra written by M. Hazewinkel and published by Elsevier. This book was released on 2008-04-18 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes
Download or read book Hopf Algebras and Tensor Categories written by Nicolás Andruskiewitsch and published by American Mathematical Soc.. This book was released on 2013-02-21 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Hopf Algebras and Tensor Categories, held July 4-8, 2011, at the University of Almeria, Almeria, Spain. The articles in this volume cover a wide variety of topics related to the theory of Hopf algebras and its connections to other areas of mathematics. In particular, this volume contains a survey covering aspects of the classification of fusion categories using Morita equivalence methods, a long comprehensive introduction to Hopf algebras in the category of species, and a summary of the status to date of the classification of Hopf algebras of dimensions up to 100. Among other topics discussed in this volume are a study of normalized class sum and generalized character table for semisimple Hopf algebras, a contribution to the classification program of finite dimensional pointed Hopf algebras, relations to the conjecture of De Concini, Kac, and Procesi on representations of quantum groups at roots of unity, a categorical approach to the Drinfeld double of a braided Hopf algebra via Hopf monads, an overview of Hom-Hopf algebras, and several discussions on the crossed product construction in different settings.
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 341 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 Groups Algebras and Applications written by César Polcino Milies and published by American Mathematical Soc.. This book was released on 2011 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory.
Download or read book New Trends in Algebras and Combinatorics written by K. P. Shum and published by . This book was released on 2020 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
