Yetter Drinfel D Hopf Algebras Over Groups Of Prime Order

Author : Yorck Sommerhäuser
Publisher : Springer
Page : 164 pages
File Size : 51,8 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540454236

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Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order by Yorck Sommerhäuser Pdf

Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.

Author : Yorck Sommerhauser
Publisher : Unknown
Page : 172 pages
File Size : 53,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662166232

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Yetter-Drinfel'd Hopf Algebras Over Groups of Prime Order by Yorck Sommerhauser Pdf

Author : Nicolás Andruskiewitsch,Juan Cuadra,Blas Torrecillas
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 45,6 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9780821875643

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Hopf Algebras and Tensor Categories by Nicolás Andruskiewitsch,Juan Cuadra,Blas Torrecillas Pdf

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.

Author : Sonia Natale
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 42,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839485

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Semisolvability of Semisimple Hopf Algebras of Low Dimension by Sonia Natale Pdf

The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.

Author : Yorck Sommerhäuser
Publisher : Springer
Page : 164 pages
File Size : 50,5 Mb
Release : 2002-07-09
Category : Mathematics
ISBN : 3540437991

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Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order by Yorck Sommerhäuser Pdf

Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.

Author : Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang
Publisher : American Mathematical Soc.
Page : 359 pages
File Size : 52,6 Mb
Release : 2021-07-06
Category : Education
ISBN : 9781470456245

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Hopf Algebras, Tensor Categories and Related Topics by Nicolás Andruskiewitsch,Gongxiang Liu,Susan Montgomery,Yinhuo Zhang Pdf

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.

Author : David E. Radford
Publisher : World Scientific
Page : 584 pages
File Size : 46,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814335997

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Hopf Algebras by David E. Radford Pdf

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.

Author : Jeffrey Bergen,Stefan Catoiu,William Chin
Publisher : CRC Press
Page : 282 pages
File Size : 44,6 Mb
Release : 2004-01-28
Category : Mathematics
ISBN : 0824755669

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Hopf Algebras by Jeffrey Bergen,Stefan Catoiu,William Chin Pdf

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.

Author : Yevgenia Kashina,Yorck Sommerhäuser,Yongchang Zhu
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 54,8 Mb
Release : 2006
Category : Cauchy integrals
ISBN : 9780821838860

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On Higher Frobenius-Schur Indicators by Yevgenia Kashina,Yorck Sommerhäuser,Yongchang Zhu Pdf

We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these invariants. In particular, we prove a version of Cauchy's theorem for semisimple Hopf algebras. Furthermore, we give some examples that illustrate the general theory.

Author : Y. Bahturin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 54,7 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.

Author : Anonim
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 44,5 Mb
Release : 2003-03-31
Category : Mathematics
ISBN : 1402012209

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Groups, Rings, Lie and Hopf Algebras by Anonim 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.

Author : M A Lifshits,Robert Coquereaux,School on "Quantum symmetries in theoretical physics and mathematics"
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 52,7 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821826553

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Quantum Symmetries in Theoretical Physics and Mathematics by M A Lifshits,Robert Coquereaux,School on "Quantum symmetries in theoretical physics and mathematics" Pdf

This volume presents articles from several lectures presented at the school on 'Quantum Symmetries in Theoretical Physics and Mathematics' held in Bariloche, Argentina. The various lecturers provided significantly different points of view on several aspects of Hopf algebras, quantum group theory, and noncommutative differential geometry, ranging from analysis, geometry, and algebra to physical models, especially in connection with integrable systems and conformal field theories. Primary topics discussed in the text include subgroups of quantum $SU(N)$, quantum ADE classifications and generalized Coxeter systems, modular invariance, defects and boundaries in conformal field theory, finite dimensional Hopf algebras, Lie bialgebras and Belavin-Drinfeld triples, real forms of quantum spaces, perturbative and non-perturbative Yang-Baxter operators, braided subfactors in operator algebras and conformal field theory, and generalized ($d^N$) cohomologies.

Author : Nicolás Andruskiewitsch,Walter Ricardo Ferrer Santos,Hans-Jürgen Schneider
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 47,6 Mb
Release : 2000
Category : Hopf algebras
ISBN : 9780821821268

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New Trends in Hopf Algebra Theory by Nicolás Andruskiewitsch,Walter Ricardo Ferrer Santos,Hans-Jürgen Schneider Pdf

This volume presents the proceedings from the Colloquium on Quantum Groups and Hopf Algebras held in Cordoba (Argentina) in 1999. The meeting brought together researchers who discussed recent developments in Hopf algebras, one of the most important being the influence of quantum groups. Articles offer introductory expositions and surveys on topics of current interest that, to date, have not been available in the current literature. Surveys are included on characteristics of Hopf algebras and their generalizations, biFrobenius algebras, braided Hopf algebras, inner actions and Galois theory, face algebras, and infinitesimal Hopf algebras. The following topics are also covered: existence of integrals, classification of semisimple and pointed Hopf algebras, *-Hopf algebras, dendriform algebras, etc. Non-classical topics are also included, reflecting its applications both inside and outside the theory.

Author : Stefaan Caenepeel
Publisher : CRC Press
Page : 352 pages
File Size : 42,5 Mb
Release : 2020-09-29
Category : Mathematics
ISBN : 9781000153286

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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 : Masaki Izumi,Hideki Kosaki
Publisher : American Mathematical Soc.
Page : 198 pages
File Size : 54,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829356

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Kac Algebras Arising from Composition of Subfactors: General Theory and Classification by Masaki Izumi,Hideki Kosaki Pdf

We deal with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying: $G=N \rtimes H$ is a semi-direct product, the induced map $g \in G \to [\alpha_g] \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism, and the restrictions $\alpha\!\!\mid_N,\alpha\!\!\mid_H$ are genuine actions of the subgroups on the factor ${\mathcal L}$. The pair ${\mathcal M}={\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal N}={\mathcal L}^{\alpha\mid_N}$ (of the crossed product ${\mathcal L} \rtimes_{\alpha} H$ and the fixed-point algebra ${\mathcal L}^{\alpha\mid_N}$) gives us an irreducible inclusion of factors with Jones index $\ No. G$. The inclusion ${\mathcal M} \supseteq {\mathcal N}$ is of depth $2$ and hence known to correspond to a Kac algebra of dimension $\ No. G$.A Kac algebra arising in this way is investigated in detail, and in fact the relevant multiplicative unitary (satisfying the pentagon equation) is described. We introduce and analyze a certain cohomology group (denoted by $H^2((N,H),{\mathbf T})$) providing complete information on the Kac algebra structure, and we construct an abundance of non-trivial examples by making use of various cocycles. The operator algebraic meaning of this cohomology group is clarified, and some related topics are also discussed. Sector technique enables us to establish structure results for Kac algebras with certain prescribed underlying algebra structure.They guarantee that 'most' Kac algebras of low dimension (say less than $60$) actually arise from inclusions of the form ${\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal L}^{\alpha\mid_N}$, and consequently their classification can be carried out by determining $H^2((N,H),{\mathbf T})$. Among other things we indeed classify Kac algebras of dimension $16$ and $24$, which (together with previously known results) gives rise to the complete classification of Kac algebras of dimension up to $31$. Partly to simplify classification procedure and hopefully for its own sake, we also study 'group extensions' of general (finite-dimensional) Kac algebras with some discussions on related topics.