Fundamentals Of Hopf Algebras
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Fundamentals Of Hopf Algebras
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Author : Robert G. Underwood
language : en
Publisher: Springer
Release Date : 2015-06-10
Fundamentals Of Hopf Algebras written by Robert G. Underwood and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-10 with Mathematics categories.
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.
Hopf Algebras And Galois Module Theory
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Author : Lindsay N. Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-10
Hopf Algebras And Galois Module Theory written by Lindsay N. Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Education categories.
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.
Groups Rings Lie And Hopf Algebras
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-03-31
Groups Rings Lie And Hopf Algebras written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-31 with Mathematics categories.
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.
Hopf Algebras In Noncommutative Geometry And Physics
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Author : Stefaan Caenepeel
language : en
Publisher: CRC Press
Release Date : 2019-05-07
Hopf Algebras In Noncommutative Geometry And Physics written by Stefaan Caenepeel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
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
Hopf Algebra
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Author : Sorin Dascalescu
language : en
Publisher: CRC Press
Release Date : 2000-09-15
Hopf Algebra written by Sorin Dascalescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-15 with Mathematics categories.
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.
Fundamentals Of Modern Algebra A Global Perspective
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Author : Robert G Underwood
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-12-28
Fundamentals Of Modern Algebra A Global Perspective written by Robert G Underwood and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-28 with Mathematics categories.
The purpose of this book is to provide a concise yet detailed account of fundamental concepts in modern algebra. The target audience for this book is first-year graduate students in mathematics, though the first two chapters are probably accessible to well-prepared undergraduates. The book covers a broad range of topics in modern algebra and includes chapters on groups, rings, modules, algebraic extension fields, and finite fields. Each chapter begins with an overview which provides a road map for the reader showing what material will be covered. At the end of each chapter we collect exercises which review and reinforce the material in the corresponding sections. These exercises range from straightforward applications of the material to problems designed to challenge the reader. We also include a list of 'Questions for Further Study' which pose problems suitable for master's degree research projects.
Algebra And Its Applications
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Author : Mohammad Ashraf
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06
Algebra And Its Applications written by Mohammad Ashraf and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-06 with Mathematics categories.
This volume showcases mostly the contributions presented at the International Conference in Algebra and Its Applications held at the Aligarh Muslim University, Aligarh, India during November 12-14, 2016. Refereed by renowned experts in the field, this wide-ranging collection of works presents the state of the art in the field of algebra and its applications covering topics such as derivations in rings, category theory, Baer module theory, coding theory, graph theory, semi-group theory, HNP rings, Leavitt path algebras, generalized matrix algebras, Nakayama conjecture, near ring theory and lattice theory. All of the contributing authors are leading international academicians and researchers in their respective fields. Contents On Structure of ∗-Prime Rings with Generalized Derivation A characterization of additive mappings in rings with involution| Skew constacyclic codes over Fq + vFq + v2Fq Generalized total graphs of commutative rings: A survey Differential conditions for which near-rings are commutative rings Generalized Skew Derivations satisfying the second Posner’s theorem on Lie ideals Generalized Skew-Derivations on Lie Ideals in Prime Rings On generalized derivations and commutativity of prime rings with involution On (n, d)-Krull property in amalgamated algebra Pure ideals in ordered Γ-semigroups Projective ideals of differential polynomial rings over HNP rings Additive central m-power skew-commuting maps on semiprime rings A Note on CESS-Lattices Properties Inherited by Direct Sums of Copies of a Module Modules witnessing that a Leavitt path algebra is directly infinite Inductive Groupoids and Normal Categories of Regular Semigroups Actions of generalized derivations in Rings and Banach Algebras Proper Categories and Their Duals On Nakayama Conjecture and related conjectures-Review On construction of global actions for partial actions On 2-absorbing and Weakly 2-absorbing Ideals in Product Lattices Separability in algebra and category theory Annihilators of power values of generalized skew derivations on Lie ideals Generalized derivations on prime rings with involution
Bimonoids For Hyperplane Arrangements
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Author : Marcelo Aguiar
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-19
Bimonoids For Hyperplane Arrangements written by Marcelo Aguiar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-19 with Mathematics categories.
The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel-Hopf, Poincar -Birkhoff-Witt, and Cartier-Milnor-Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.
Coxeter Bialgebras
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Author : Marcelo Aguiar
language : en
Publisher: Cambridge University Press
Release Date : 2022-11-17
Coxeter Bialgebras written by Marcelo Aguiar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-17 with Mathematics categories.
The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.
Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View
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Author : Gabriella Böhm
language : en
Publisher: Springer
Release Date : 2018-11-01
Hopf Algebras And Their Generalizations From A Category Theoretical Point Of View written by Gabriella Böhm and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-01 with Mathematics categories.
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.