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Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension

2020-06-22 Mathematics
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Release : 2020-06-22
Genre : Mathematics
Kind : eBook
Book Rating : 130/5 ( reviews)

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Book Synopsis Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension by : Aidan Sims

Download or read book Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension written by Aidan Sims. This book was released on 2020-06-22. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the notes of the lectures given at the Advanced Course on Crossed Products, Groupoids, and Rokhlin dimension, that took place at the Centre de Recerca Matemàtica (CRM) from March 13 to March 17, 2017. The notes consist of three series of lectures. The first one was given by Dana Williams (Dartmouth College), and served as an introduction to crossed products of C*-algebras and the study of their structure. The second series of lectures was delivered by Aidan Sims (Wollongong), who gave an overview of the theory of topological groupoids (as a model for groups and group actions) and groupoid C*-algebras, with particular emphasis on the case of étale groupoids. Finally, the last series was delivered by Gábor Szabó (Copenhagen), and consisted of an introduction to Rokhlin type properties (mostly centered around the work of Hirshberg, Winter and Zacharias) with hints to the more advanced theory related to groupoids.

Operator Algebra and Dynamics

2013-12-03 Mathematics
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Release : 2013-12-03
Genre : Mathematics
Kind : eBook
Book Rating : 590/5 ( reviews)

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Book Synopsis Operator Algebra and Dynamics by : Toke M. Carlsen

Download or read book Operator Algebra and Dynamics written by Toke M. Carlsen. This book was released on 2013-12-03. Available in PDF, EPUB and Kindle. Book excerpt: Based on presentations given at the NordForsk Network Closing Conference “Operator Algebra and Dynamics,” held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.

Crossed Products of Operator Algebras

2019-04-10 C*-algebras
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Release : 2019-04-10
Genre : C*-algebras
Kind : eBook
Book Rating : 454/5 ( reviews)

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Book Synopsis Crossed Products of Operator Algebras by : Elias G. Katsoulis

Download or read book Crossed Products of Operator Algebras written by Elias G. Katsoulis. This book was released on 2019-04-10. Available in PDF, EPUB and Kindle. Book excerpt: The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.

Recent Advances in Operator Theory and Operator Algebras

2017-08-07 Mathematics
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Release : 2017-08-07
Genre : Mathematics
Kind : eBook
Book Rating : 611/5 ( reviews)

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Book Synopsis Recent Advances in Operator Theory and Operator Algebras by : Hari Bercovici

Download or read book Recent Advances in Operator Theory and Operator Algebras written by Hari Bercovici. This book was released on 2017-08-07. Available in PDF, EPUB and Kindle. Book excerpt: This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.

Crossed Products of $C^*$-Algebras

2007 Mathematics
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Release : 2007
Genre : Mathematics
Kind : eBook
Book Rating : 420/5 ( reviews)

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Book Synopsis Crossed Products of $C^*$-Algebras by : Dana P. Williams

Download or read book Crossed Products of $C^*$-Algebras written by Dana P. Williams. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. in addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. in particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. to view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.

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