Group Theory And Hopf Algebras

Author : A. P. Balachandran,S. G. Jo,Giuseppe Marmo
Publisher : World Scientific
Page : 270 pages
File Size : 55,6 Mb
Release : 2010
Category : Science
ISBN : 9789814322201

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Group Theory and Hopf Algebras by A. P. Balachandran,S. G. Jo,Giuseppe Marmo Pdf

This book is addressed to graduate students and research workers in theoretical physics who want a thorough introduction to group theory and Hopf algebras. It is suitable for a one-semester course in group theory or a two-semester course which also treats advanced topics. Starting from basic definitions, it goes on to treat both finite and Lie groups as well as Hopf algebras. Because of the diversity in the choice of topics, which does not place undue emphasis on finite or Lie groups, it should be useful to physicists working in many branches. A unique aspect of the book is its treatment of Hopf algebras in a form accessible to physicists. Hopf algebras are generalizations of groups and their concepts are acquiring importance in the treatment of conformal field theories, noncommutative spacetimes, topological quantum computation and other important domains of investigation. But there is a scarcity of treatments of Hopf algebras at a level and in a manner that physicists are comfortable with. This book addresses this need superbly. There are illustrative examples from physics scattered throughout the book and in its set of problems. It also has a good bibliography. These features should enhance its value to readers. The authors are senior physicists with considerable research and teaching experience in diverse aspects of fundamental physics. The book, being the outcome of their combined efforts, stands testament to their knowledge and pedagogical skills.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814464161

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Group Theory and Hopf Algebras by Anonim Pdf

Author : Stefaan Caenepeel,Freddy Van Oystaeyen
Publisher : CRC Press
Page : 332 pages
File Size : 47,8 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9780429529986

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Hopf Algebras and Quantum Groups by Stefaan Caenepeel,Freddy Van Oystaeyen Pdf

This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum g

Author : Stefaan Caenepeel
Publisher : CRC Press
Page : 128 pages
File Size : 41,9 Mb
Release : 2020-09-30
Category : Mathematics
ISBN : 9781000116731

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Rings, Hopf Algebras, and Brauer Groups by Stefaan Caenepeel Pdf

"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. "

Author : Thomas Timmermann
Publisher : European Mathematical Society
Page : 436 pages
File Size : 53,6 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190434

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An Invitation to Quantum Groups and Duality by Thomas Timmermann Pdf

This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of $C^*$-algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, Baaj-Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, $C^*$-algebras, and von Neumann algebras.

Author : Stefaan Caenepeel
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 46,8 Mb
Release : 2002-03-31
Category : Mathematics
ISBN : 1402003463

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Brauer Groups, Hopf Algebras and Galois Theory by Stefaan Caenepeel Pdf

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.

Author : H. Yanagihara
Publisher : Springer
Page : 315 pages
File Size : 47,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540370772

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Theory of Hopf Algebras Attached to Group Schemes by H. Yanagihara Pdf

Author : A. V. Zelevinsky
Publisher : Springer
Page : 189 pages
File Size : 48,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387114

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Representations of Finite Classical Groups by A. V. Zelevinsky Pdf

Author : Pierre Cartier,Frédéric Patras
Publisher : Springer Nature
Page : 277 pages
File Size : 52,6 Mb
Release : 2021-09-20
Category : Mathematics
ISBN : 9783030778453

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Classical Hopf Algebras and Their Applications by Pierre Cartier,Frédéric Patras Pdf

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.

Author : Lindsay Childs
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 41,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821810774

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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders by Lindsay Childs Pdf

This book gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.

Author : Robert G. Underwood
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 52,9 Mb
Release : 2011-08-30
Category : Mathematics
ISBN : 9780387727653

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An Introduction to Hopf Algebras by Robert G. Underwood Pdf

Only book on Hopf algebras aimed at advanced undergraduates

Author : Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 55,8 Mb
Release : 2021-11-10
Category : Education
ISBN : 9781470465162

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Hopf Algebras and Galois Module Theory by Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood Pdf

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 : Shahn Majid
Publisher : Cambridge University Press
Page : 668 pages
File Size : 55,7 Mb
Release : 2000
Category : Group theory
ISBN : 0521648688

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Foundations of Quantum Group Theory by Shahn Majid Pdf

A graduate level text which systematically lays out the foundations of Quantum Groups.

Author : Stephen U. Chase,Moss E. Sweedler
Publisher : Springer
Page : 139 pages
File Size : 53,6 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540361343

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Hopf Algebras and Galois Theory by Stephen U. Chase,Moss E. Sweedler Pdf

Author : Y. Bahturin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 42,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302353

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Groups, Rings, Lie and Hopf Algebras by Y. Bahturin Pdf

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.