2010/09/25 by Jerome Kaminker, Ian F. Putnam, Michael F. Whittaker
Mathematics · #Advanced Operator Algebra Research #Conjecture #Duality (order theory) #Dynamical system (definition) #Dynamical systems theory #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Noncommutative geometry #math.DS #math.KT #math.OA #msc:37B10 #msc:37D40 #msc:46L35 #msc:46L80
paper · pdf · doi:10.1515/crelle-2014-0126
published as J. reine angew. Math. 730 (2017), 263-299 · 36 pages
arxiv created 2010/09/25 · openalex publication_date 2015/02/05 · openalex created_date 2016/06/24 · arxiv updated 2017/09/25 · openalex updated_date 2026/08/05
Abstract The K-theoretic analog of Spanier–Whitehead duality for noncommutative <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>C</m:mi> <m:mo>*</m:mo> </m:msup> </m:math> C* -algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces. This had previously been proved only for shifts of finite type. Implications of this result as well as relations to the Baum–Connes conjecture and other topics are also considered.