Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012 (Springer Proceedings in Mathematics & Statistics Book 58)

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. 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. 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. Edited By Toke M. Carlsen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov. 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. Front Matter....Pages i-xvi The Haagerup Property for Discrete Measured Groupoids....Pages 1-30 Do Phantom Cuntz-Krieger Algebras Exist?....Pages 31-40 Projective Dimension in Filtrated K-Theory....Pages 41-62 An Introduction to the C ∗ -Algebra of a One-Sided Shift Space....Pages 63-88 Classification of Graph C ∗ -Algebras with No More than Four Primitive Ideals....Pages 89-129 Remarks on the Pimsner-Voiculescu Embedding....Pages 131-140 Graph C ∗ -Algebras with a T 1 Primitive Ideal Space....Pages 141-156 The Law of Large Numbers for the Free Multiplicative Convolution....Pages 157-186 Is Every Irreducible Shift of Finite Type Flow Equivalent to a Renewal System?....Pages 187-209 On the Grothendieck Theorem for Jointly Completely Bounded Bilinear Forms....Pages 211-221 C ∗ -Algebras Associated with a -adic Numbers....Pages 223-238 The Structure of Stacey Crossed Products by Endomorphisms....Pages 239-252 Quasi-symmetric Group Algebras and C ∗ -Completions of Hecke Algebras....Pages 253-271 Dynamics, Wavelets, Commutants and Transfer Operators Satisfying Crossed Product Type Commutation Relations....Pages 273-293 On a Counterexample to a Conjecture by Blackadar....Pages 295-303 The Topological Dimension of Type I C ∗ -Algebras....Pages 305-328 Back Matter....Pages 329-332