Groupoids Inverse Semigroups And Their Operator Algebras
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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.
Groupoids Inverse Semigroups And Their Operator Algebras
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Author : Alan L. T. Paterson
language : en
Publisher:
Release Date : 1999
Groupoids Inverse Semigroups And Their Operator Algebras written by Alan L. T. Paterson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Groupoids categories.
Inverse Semigroups The Theory Of Partial Symmetries
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Author : Mark V Lawson
language : en
Publisher: World Scientific
Release Date : 1998-11-06
Inverse Semigroups The Theory Of Partial Symmetries written by Mark V Lawson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-06 with Mathematics categories.
Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.
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.
Characterizing Groupoid C Algebras Of Non Hausdorff Tale Groupoids
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Author : Ruy Exel
language : en
Publisher: Springer Nature
Release Date : 2022-10-18
Characterizing Groupoid C Algebras Of Non Hausdorff Tale Groupoids written by Ruy Exel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-18 with Mathematics categories.
This book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces. Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the Kumjian–Renault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the Kumjian–Renault theory to a much broader class of C*-algebras. This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.
Semigroups Categories And Partial Algebras
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Author : P. G. Romeo
language : en
Publisher: Springer Nature
Release Date : 2021-03-26
Semigroups Categories And Partial Algebras written by P. G. Romeo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-26 with Mathematics categories.
This book is a collection of selected papers presented at the International Conference on Semigroups and Applications, held at the Cochin University of Science and Technology, India, from December 9–12, 2019. This book discusses the recent developments in semigroups theory, category theory and the applications of these in various areas of research, including structure theory of semigroups, lattices, rings and partial algebras. This book presents chapters on ordering orders and quotient rings, block groups and Hall’s relations, quotients of the Booleanization of inverse semigroup, Markov chains through semigroup graph expansions, polycyclic inverse monoids and Thompson group, balanced category and bundle category. This book will be of much value to researchers working in areas of semigroup and operator theory.
Operator Theory Operator Algebras And Matrix Theory
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Author : Carlos André
language : en
Publisher: Birkhäuser
Release Date : 2018-08-22
Operator Theory Operator Algebras And Matrix Theory written by Carlos André and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-22 with Mathematics categories.
This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.
Wagner S Theory Of Generalised Heaps
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Author : Christopher D. Hollings
language : en
Publisher: Springer
Release Date : 2017-09-09
Wagner S Theory Of Generalised Heaps written by Christopher D. Hollings and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-09 with Mathematics categories.
The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts. This book contains the first translation from Russian into English of a selection of Wagner’s papers, the ideas of which are connected to present-day mathematical research. Along with a translation of Wagner’s main work in this area, his 1953 paper ‘Theory of generalised heaps and generalised groups,’ the book also includes translations of three short precursor articles that provide additional context for his major work. Researchers and students interested in both algebra (in particular, heaps, semiheaps, generalised heaps, semigroups, and groups) and differential geometry will benefit from the techniques offered by these translations, owing to the natural connections between generalised heaps and generalised groups, and the role played by these concepts in differential geometry. This book gives examples from present-day mathematics where ideas related to Wagner’s have found fruitful applications.
Introduction To Vertex Operator Algebras And Their Representations
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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
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 2004 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.
Trends In Banach Spaces And Operator Theory
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Author : Anna Kamińska
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Trends In Banach Spaces And Operator Theory written by Anna Kamińska 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 2003 with Mathematics categories.
This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.