Algebraic Structures And Their Representations

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The Latin-American conference on algebra, the XV Coloquio Latinoamericano de Algebra (Cocoyoc, Mexico), consisted of plenary sessions of general interest and special sessions on algebraic combinatorics, associative rings, cohomology of rings and algebras, commutative algebra, group representations, Hopf algebras, number theory, quantum groups, and representation theory of algebras. This proceedings volume contains original research papers related to talks at the colloquium. In addition, there are several surveys presenting important topics to a broad mathematical audience. There are also two invited papers by Raymundo Bautista and Roberto Martinez, founders of the Mexican school of representation theory of algebras. The book is suitable for graduate students and researchers interested in algebra.

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Genre : Mathematics
Author : José Antonio de la Peña
Publisher : American Mathematical Soc.
Release : 2005
File : 466 Pages
ISBN-13 : 9780821836309


Introduction To Vertex Operator Algebras And Their Representations

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* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

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Genre : Mathematics
Author : James Lepowsky
Publisher : Springer Science & Business Media
Release : 2012-12-06
File : 330 Pages
ISBN-13 : 9780817681869


Fundamentals Of Fuzzy Sets

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Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.

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Genre : Mathematics
Author : Didier Dubois
Publisher : Springer Science & Business Media
Release : 2012-12-06
File : 660 Pages
ISBN-13 : 9781461544296


Fuzzy Logic In Artificial Intelligence

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This thoroughly refereed and well organized collection of papers is largely based on papers originally presented at the IJCAI'95 Workshop on Fuzzy Logic in AI, held in Montreal, Canada, in August 1995. Additionally, a few papers were invited in order to round off the scope and competent coverage of relevant topics. The 20 revised full papers included are organized in sections on hybrid and novel architectures, machine learning and data mining, image processing and computer vision, and theoretical developments. Focusing on the most pressing problems of AI, the volume supports the view that fuzzy systems combined with traditional AI leads the move towards the next generation of intelligent systems.

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Genre : Mathematics
Author : Trevor Martin
Publisher : Springer Science & Business Media
Release : 1997-01-22
File : 294 Pages
ISBN-13 : 3540624740


Representations Of Algebraic Groups Quantum Groups And Lie Algebras

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Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.

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Genre : Mathematics
Author : Georgia Benkart
Publisher : American Mathematical Soc.
Release : 2006
File : 270 Pages
ISBN-13 : 9780821839249


A Physicists Introduction To Algebraic Structures

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Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.

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Genre : Mathematics
Author : Palash B. Pal
Publisher : Cambridge University Press
Release : 2019-05-23
File : 717 Pages
ISBN-13 : 9781108492201


Linear Algebraic Groups And Their Representations

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* Brings together a wide variety of themes under a single unifying perspective The proceedings of a conference on Linear algebraic Groups and their Representations - the text gets to grips with the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics.

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Genre : Mathematics
Author : Richard S. Elman
Publisher : American Mathematical Soc.
Release : 1993
File : 215 Pages
ISBN-13 : 9780821851616


Algebra Without Borders Classical And Constructive Nonassociative Algebraic Structures

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This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics. In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering. Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm.

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Genre : Mathematics
Author : Mahouton Norbert Hounkonnou
Publisher : Springer Nature
Release : 2023-12-01
File : 600 Pages
ISBN-13 : 9783031393341


An Introduction To Groups Groupoids And Their Representations

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This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.

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Genre : Mathematics
Author : Alberto Ibort
Publisher : CRC Press
Release : 2019-10-28
File : 279 Pages
ISBN-13 : 9781351869560


Recent Advances In Representation Theory Quantum Groups Algebraic Geometry And Related Topics

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This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

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Genre : Mathematics
Author : Pramod M. Achar
Publisher : American Mathematical Society
Release : 2014-08-27
File : 296 Pages
ISBN-13 : 9780821898529