Algebraic Structures And Their Representations

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Algebraic Structures And Their Representations

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Author : José Antonio de la Peña
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Algebraic Structures And Their Representations written by José Antonio de la Peña 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 2005 with Mathematics categories.

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.

Algebraic Structures And Operators Calculus

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Author : P. Feinsilver
language : en
Publisher: Springer Science & Business Media
Release Date : 1993

Algebraic Structures And Operators Calculus written by P. Feinsilver 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 1993 with Computers categories.

Introduction I. General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 II. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 III. Lie algebras: some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 II. Holomorphic canonical calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 III. Canonical Appell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 II. Dual representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 III. Matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 IV. Induced representations and homogeneous spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 General Appell systems Chapter 3 I. Convolution and stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 II. Stochastic processes on Lie groups . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 46 III. Appell systems on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 II. Induced representation and coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 III. Orthogonal polynomials in several variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 II. Finite-difference algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 III. q-HW algebra and basic hypergeometric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 IV. su2 and Krawtchouk polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 V. e2 and Lommel polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 II. Type-H Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Vll III. Upper-triangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 125 IV. Affine and Euclidean algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Chapter 7 Hermitian symmetric spaces I. Basic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 II. Space of rectangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 III. Space of skew-symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 IV. Space of symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Chapter 8 Properties of matrix elements I. Addition formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 II. Recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 III. Quotient representations and summation formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Chapter 9 Symbolic computations I. Computing the pi-matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 II. Adjoint group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 III. Recursive computation of matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Algebraic Structures

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Author : George R. Kempf
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebraic Structures written by George R. Kempf 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 2012-12-06 with Mathematics categories.

The laws of composition include addition and multiplication of numbers or func tions. These are the basic operations of algebra. One can generalize these operations to groups where there is just one law. The theory of this book was started in 1800 by Gauss, when he solved the 2000 year-old Greek problem about constructing regular n-gons by ruler and compass. The theory was further developed by Abel and Galois. After years of development the theory was put in the present form by E. Noether and E. Artin in 1930. At that time it was called modern algebra and concentrated on the abstract exposition of the theory. Nowadays there are too many examples to go into their details. I think the student should study the proofs of the theorems and not spend time looking for solutions to tricky exercises. The exercises are designed to clarify the theory. In algebra there are four basic structures; groups, rings, fields and modules. We present the theory of these basic structures. Hopefully this will give a good introduc tion to modern algebra. I have assumed as background that the reader has learned linear algebra over the real numbers but this is not necessary.

Basics Of Representation Theory

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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.

A Physicists Introduction To Algebraic Structures

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Author : Palash B. Pal
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-23

A Physicists Introduction To Algebraic Structures written by Palash B. Pal 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 2019-05-23 with Mathematics categories.

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

An Introduction To Algebraic Structures

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Author : Joseph Landin
language : en
Publisher: Courier Corporation
Release Date : 2012-08-29

An Introduction To Algebraic Structures written by Joseph Landin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.

This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.

Introduction To Vertex Operator Algebras And Their Representations

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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Vertex Operator Algebras And Their Representations written by James Lepowsky 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 2012-12-06 with Mathematics categories.

* 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.

Fundamentals Of Fuzzy Sets

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Author : Didier Dubois
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Fundamentals Of Fuzzy Sets written by Didier Dubois 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 2012-12-06 with Mathematics categories.

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.

Fuzzy Logic In Artificial Intelligence

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Author : Trevor Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-22

Fuzzy Logic In Artificial Intelligence written by Trevor Martin 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 1997-01-22 with Mathematics categories.

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.

Symmetries Unveiled

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Author : Oliver Vella
language : en
Publisher: eBookIt.com
Release Date : 2025-02-27

Symmetries Unveiled written by Oliver Vella and has been published by eBookIt.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-27 with Mathematics categories.

Exploring the Mysteries of Representation Theory Dive into the fascinating universe of symmetries and representations, where mathematics unravels the secrets of the universe. Symmetries Unveiled: A Journey Through Representation Theory invites readers on a thrilling expedition through the intricate landscape of mathematical theory and its profound impact on science. As you embark on this mathematical voyage, you'll uncover foundational concepts and historical development behind representation theory. From the elegant symmetries of groups to the groundbreaking applications of linear representations, this book is your gateway to a deeper understanding of the subject. Through chapters dedicated to Lie algebras, root systems, and quantum groups, the narrative weaves a tapestry of knowledge that connects abstract theory with real-world applications. Imagine navigating the compelling world of Kac-Moody algebras, discovering the role of crystal bases, and unlocking the mysteries of non-linear realisations. Each chapter promises to ignite curiosity with insights into symmetries in quantum mechanics and their implications in modern physics. Whether you're captivated by symmetry breaking or intrigued by the concept of duality, this book offers a profound exploration of these topics and more. Symmetries Unveiled is not just a book for mathematicians; it's a treasure trove for anyone passionate about the interplay between theory and application in theoretical physics. With chapters on computational approaches, educational techniques, and interdisciplinary impacts, it also serves as a comprehensive guide for educators and researchers alike. The culmination of the journey is an exploration of open problems and philosophical insights, paving the way for future exploration and discovery. Join this intellectual adventure and let Symmetries Unveiled transform your understanding of the mathematical principles that underpin the very fabric of reality.