Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012

ISBN-13: 9783642394584 / Angielski / Twarda / 2013 / 332 str.

Toke M. Carlsen;Søren Eilers;Gunnar Restorff

Opis

Based on presentations given at the NordForsk Network Closing Conference "Operator Algebra and Dynamics," held in Gjaargarour, 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.

Spis treści

1 The Haagerup property for discrete measured groupoids: Claire Anantharaman-Delaroche.- 2 Do phantom Cuntz-Krieger algebras exist? Sara E. Arklint.- 3 Projective dimension in filtrated K-theory: Rasmus Bentmann.- 4 An introduction to the C_-algebra of a one-sided shift space: Toke Meier Carlsen.- 5 Classification of graph C_-algebras with no more than four primitive ideals: Søren Eilers, Gunnar Restorff, and Efren Ruiz.- 6 Remarks on the Pimsner-Voiculescu embedding: George A. Elliott and Zhuang Niu.- 7 Graph C_-algebras with a T1 primitive ideal space: James Gabe.- 8 The law of large numbers for the free multiplicative convolution: Uffe Haagerup and Sören Möller.- 9 Is every irreducible shift of finite type flow equivalent to a renewal system? Rune Johansen.- 10 On the Grothendieck Theorem for jointly completely bounded bilinear forms: Tim de Laat.- 11 C_-algebras associated with a-adic numbers: Tron Omland.- 12 The structure of Stacey crossed products by endomorphisms: Eduard Ortega and Enrique Pardo.- 13 Quasi-symmetric group algebras and C_-completions of Hecke algebras: Rui Palma.- 14 Dynamics, wavelets, commutants and transfer operators satisfying crossed product type commutation relations: Sergei Silvestrov.- 15 On a counterexample to a conjecture by Blackadar: Adam P. W. Sørensen.- 16 The topological dimension of type I C_-algebras: Hannes Thiel.- Index.

Blurb

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.