Introduction To Coalgebra

Author : Bart Jacobs
Publisher : Unknown
Page : 477 pages
File Size : 45,7 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 1316838560

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Introduction to Coalgebra by Bart Jacobs Pdf

Author : Bart Jacobs
Publisher : Cambridge University Press
Page : 495 pages
File Size : 44,6 Mb
Release : 2017
Category : Mathematics
ISBN : 9781107177895

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Introduction to Coalgebra by Bart Jacobs Pdf

An accessible introduction to coalgebra, with clear mathematical explanations and numerous examples and exercises.

Author : Klaus Denecke,Shelly L. Wismath
Publisher : World Scientific
Page : 291 pages
File Size : 44,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812837455

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Universal Algebra and Coalgebra by Klaus Denecke,Shelly L. Wismath Pdf

The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.

Author : Jeffrey Bergen,Stefan Catoiu,William Chin
Publisher : CRC Press
Page : 282 pages
File Size : 41,6 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 : Alexander Kurz,Marina Lenisa
Publisher : Springer
Page : 457 pages
File Size : 50,6 Mb
Release : 2009-09-19
Category : Computers
ISBN : 9783642037412

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Algebra and Coalgebra in Computer Science by Alexander Kurz,Marina Lenisa Pdf

This book constitutes the proceedings of the Third International Conference on Algebra and Coalgebra in Computer Science, CALCO 2009, formed in 2005 by joining CMCS and WADT. This year the conference was held in Udine, Italy, September 7-10, 2009. The 23 full papers were carefully reviewed and selected from 42 submissions. They are presented together with four invited talks and workshop papers from the CALCO-tools Workshop. The conference was divided into the following sessions: algebraic effects and recursive equations, theory of coalgebra, coinduction, bisimulation, stone duality, game theory, graph transformation, and software development techniques.

Author : Sorin Dascalescu,Constantin Nastasescu,Serban Raianu
Publisher : CRC Press
Page : 420 pages
File Size : 49,7 Mb
Release : 2000-09-15
Category : Mathematics
ISBN : 9781482270747

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Hopf Algebra by Sorin Dascalescu,Constantin Nastasescu,Serban Raianu Pdf

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.

Author : L.A. Lambe,D.E. Radford
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 45,9 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9781461541097

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Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach by L.A. Lambe,D.E. Radford Pdf

Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in [Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic example of a coalgebra for our purposes and is at the heart of most algebraic constructions described in this book. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum groups.

Author : Reiko Heckel,Stefan Milius
Publisher : Springer
Page : 370 pages
File Size : 48,5 Mb
Release : 2013-08-27
Category : Computers
ISBN : 9783642402067

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Algebra and Coalgebra in Computer Science by Reiko Heckel,Stefan Milius Pdf

This book constitutes the refereed proceedings of the 5th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 full papers presented together with 4 invited talks were carefully reviewed and selected from 33 submissions. The papers cover topics in the fields of abstract models and logics, specialized models and calculi, algebraic and coalgebraic semantics, system specification and verification, as well as corecursion in programming languages, and algebra and coalgebra in quantum computing. The book also includes 6 papers from the CALCO Tools Workshop, co-located with CALCO 2013 and dedicated to tools based on algebraic and/or coalgebraic principles.

Author : Davide Sangiorgi,Robert de Simone
Publisher : Springer Science & Business Media
Page : 678 pages
File Size : 47,5 Mb
Release : 1998-08-19
Category : Computers
ISBN : 3540648968

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CONCUR '98 Concurrency Theory by Davide Sangiorgi,Robert de Simone Pdf

This book constitutes the refereed proceedings of the 9th International Conference on Concurrency Theory, CONCUR'98, held in Nice, France, in September 1998. The 35 revised full papers presented were carefully selected from a total of 104 submissions. Also presented are five invited contributions. Among the topics covered are moduls of computation and semantic domains, process algebras, Petri Nets, event structures, real-time systems, hybrid systems, model checking, verification techniques, refinement, rewriting, typing systems and algorithms, etc..

Author : I. Gohberg,P. Lancaster,P.N. Shivakumar
Publisher : Birkhäuser
Page : 448 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890359

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Recent Developments in Operator Theory and Its Applications by I. Gohberg,P. Lancaster,P.N. Shivakumar Pdf

The papers selected for publication here, many of them written by leaders in the field, bring readers up to date on recent achievements in modern operator theory and applications. The book’s subject matter is of practical use to a wide audience in mathematical and engineering sciences.

Author : George M. Bergman
Publisher : Springer
Page : 572 pages
File Size : 55,7 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9783319114781

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An Invitation to General Algebra and Universal Constructions by George M. Bergman Pdf

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 48,5 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410

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Tensor Categories by Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik Pdf

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.

Author : Mogens Nielsen,Uffe Engberg
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 40,8 Mb
Release : 2002-03-22
Category : Computers
ISBN : 9783540433668

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Foundations of Software Science and Computation Structures by Mogens Nielsen,Uffe Engberg Pdf

ETAPS 2002 is the ?fth instance of the European Joint Conferences on Theory and Practice of Software. ETAPS is an annual federated conference that was established in 1998by combining a number of existing and new conferences. This year it comprises ?ve conferences (FOSSACS, FASE, ESOP, CC, TACAS), thirteen satellite workshops (ACL2, AGT, CMCS, COCV, DCC, INT, LDTA, SC, SFEDL, SLAP, SPIN, TPTS and VISS), eight invited lectures (not including those that are speci?c to the satellite events), and several tutorials. The events that comprise ETAPS address various aspects of the system - velopment process, including speci?cation, design, implementation, analysis and improvement. The languages, methodologies and tools which support these - tivities are all well within its scope. Di?erent blends of theory and practice are represented, with an inclination towards theory with a practical motivation on one hand and soundly-based practice on the other. Many of the issues involved in software design apply to systems in general, including hardware systems, and the emphasis on software is not intended to be exclusive.

Author : Christian Kassel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207832

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Quantum Groups by Christian Kassel Pdf

Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.

Author : Jeffrey Bergen,Stefan Catoiu,William Chin
Publisher : CRC Press
Page : 200 pages
File Size : 41,9 Mb
Release : 2004-01-28
Category : Mathematics
ISBN : 9781482293159

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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