C Algebras And Elliptic Theory

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C Algebras And Elliptic Theory

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Author : Bogdan Bojarski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-09

C Algebras And Elliptic Theory written by Bogdan Bojarski 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 2006-11-09 with Mathematics categories.

This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.

C Algebras And Elliptic Theory Ii

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Author : Dan Burghelea
language : en
Publisher: Birkhäuser
Release Date : 2008-02-18

C Algebras And Elliptic Theory Ii written by Dan Burghelea and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-18 with Mathematics categories.

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

An Invitation To C Algebras

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Author : W. Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Invitation To C Algebras written by W. Arveson 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.

This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2.

Representation Theories And Algebraic Geometry

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Author : A. Broer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Representation Theories And Algebraic Geometry written by A. Broer 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 2013-03-09 with Mathematics categories.

The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.

Hilbert C Modules

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Author : Vladimir Markovich Manuĭlov
language : en
Publisher: American Mathematical Soc.
Release Date :

Hilbert C Modules written by Vladimir Markovich Manuĭlov 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 with Mathematics categories.

Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert $C*$-modules. Hilbert $C*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C $ is replaced by an arbitrary $C*$-algebra. The general theory of Hilbert $C*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool inoperator algebras theory, index theory of elliptic operators, $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C*$-modules is interesting on its own. In this book, the authors explain in detail the basic notions and results of thetheory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.

From Differential Geometry To Non Commutative Geometry And Topology

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Author : Neculai S. Teleman
language : en
Publisher: Springer Nature
Release Date : 2019-11-10

From Differential Geometry To Non Commutative Geometry And Topology written by Neculai S. Teleman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-10 with Mathematics categories.

This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.

Superstrings Geometry Topology And C Algebras

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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-13

Superstrings Geometry Topology And C Algebras 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 2010-10-13 with Mathematics categories.

This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in $K$-homology and twisted $K$-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models, $C^*$-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of $C^*$-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.

Operator Algebras And Applications Part 1

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Author : Richard V. Kadison
language : en
Publisher: American Mathematical Soc.
Release Date : 1982

Operator Algebras And Applications Part 1 written by Richard V. Kadison 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 1982 with Mathematics categories.

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Author :
language : en
Publisher: World Scientific
Release Date :

written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Operator Theory Systems Theory And Scattering Theory Multidimensional Generalizations

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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Operator Theory Systems Theory And Scattering Theory Multidimensional Generalizations written by Daniel Alpay 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 2006-03-30 with Mathematics categories.

This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.