An Introduction To Groups Groupoids And Their Representations
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An Introduction To Groups Groupoids And Their Representations
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Author : Alberto Ibort
language : en
Publisher: CRC Press
Release Date : 2019-10-28
An Introduction To Groups Groupoids And Their Representations written by Alberto Ibort and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-28 with Mathematics categories.
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.
An Introduction To Groups Groupoids And Their Representations
DOWNLOAD
Author : Alberto Ibort
language : en
Publisher: CRC Press
Release Date : 2019-10-28
An Introduction To Groups Groupoids And Their Representations written by Alberto Ibort and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-28 with Mathematics categories.
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.
Glossary Of Morphology
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Author : Federico Vercellone
language : en
Publisher: Springer Nature
Release Date : 2020-12-01
Glossary Of Morphology written by Federico Vercellone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Philosophy categories.
This book is a significant novelty in the scientific and editorial landscape. Morphology is both an ancient and a new discipline that rests on Goethe's heritage and re-forms it in the present through the concepts of form and image. The latter are to be understood as structural elements of a new cultural grammar able to make the late modern world intelligible. In particular, compared to the original Goethean project, but also to C.P. Snow's idea of unifying the “two cultures”, the fields of morphological culture that are the object of this glossary have profoundly changed. The ever-increasing importance of the image as a polysemic form has made the two concepts absolutely transitive, so to speak. This is concomitant with the emergence of a culture that revolves around the image, attracting the verbal logos into its orbit. Incidentally, even the hermeneutic relationship between past and present relies more and more on the image, causing deep changes in cultural environments. Form and image are not just bridging concepts, as in the field of ancient morphology, but real transitive concepts that define the state of a culture. From the Internet to smartphones, television, advertising, etc., we are witnessing – as Horst Bredekamp observes – an immense mass of images that fill our time and affect the most diverse areas of our culture. The ancient connection between science and art recalled by Goethe emerges with unusual evidence thanks to intersecting patterns and expressive forms that are sometimes shared by different forms of knowledge. Creating a glossary and a culture of these intersections is the task of morphology, which thus enters into the boundaries between aesthetics, art, design, advertising, and sciences (from mathematics to computer science, to physics, and to biology), in order to provide the founding elements of a grammar and a syntax of the image. The latter, in its formal quality, both expressive and symbolic, is a fundamental element in the unification of the various kinds of knowledge, which in turn come to be configured, in this regard, also as styles of vision. The glossary is subdivided into contiguous sections, within a complex framework of cross-references. In addition to the two curators, the book features the collaboration of a team of scholars from the individual disciplines appearing in the glossary.
Geometric Science Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Geometric Science Of Information written by Frank Nielsen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Computers categories.
This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.
Representation Theory Of Finite Groups
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Author : Benjamin Steinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-23
Representation Theory Of Finite Groups written by Benjamin Steinberg 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 2011-10-23 with Mathematics categories.
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Group Representations Ergodic Theory And Mathematical Physics
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Group Representations Ergodic Theory And Mathematical Physics written by Robert S. Doran 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 2008 with Mathematics categories.
George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.
Groupoids Inverse Semigroups And Their Operator Algebras
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Author : Alan Paterson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Groupoids Inverse Semigroups And Their Operator Algebras written by Alan Paterson 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.
In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.
Representations Of Algebras Geometry And Physics
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Author : Kiyoshi Igusa
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-05-17
Representations Of Algebras Geometry And Physics written by Kiyoshi Igusa 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 2021-05-17 with Education categories.
This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called “geodesic ghor algebras”, a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t t-structure, and an introduction to methods of constructive category theory.
Tool Kit For Groupoid C Algebras
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Author : Dana P. Williams
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-24
Tool Kit For Groupoid C Algebras written by Dana P. Williams 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 2019-09-24 with Mathematics categories.
The construction of a C∗-algebra from a locally compact groupoid is an important generalization of the group C∗-algebra construction and of the transformation group C∗-algebra construction. Since their introduction in 1980, groupoid C∗-algebras have been intensively studied with diverse applications, including graph algebras, classification theory, variations on the Baum-Connes conjecture, and noncommutative geometry. This book provides a detailed introduction to this vast subject and is suitable for graduate students or any researcher who wants to use groupoid C∗-algebras in their work. The main focus is to equip the reader with modern versions of the basic technical tools used in the subject, which will allow the reader to understand fundamental results and make contributions to various areas in the subject. Thus, in addition to covering the basic properties and construction of groupoid C∗-algebras, the focus is to give a modern treatment of some of the major developments in the subject in recent years, including the Equivalence Theorem and the Disintegration Theorem. Also covered are the complicated subjects of amenability of groupoids and simplicity results. The book is reasonably self-contained and accessible to graduate students with a good background in operator algebras.
Representations Of Groups
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Author : Klaus Lux
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-01
Representations Of Groups written by Klaus Lux 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 2010-07-01 with Mathematics categories.
The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from www.gap-system.org and readers can download source code and solutions to selected exercises from the book's web page.