2000/12/12 by Ruy Exel, Exel, Ruy · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.DS #math.OA
paper · pdf · doi:10.48550/arxiv.math/0012084
14 pages, Plain TeX
arxiv created 2000/12/12 · openalex publication_date 2000/12/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new definition for the crossed-product of a C*-algebra A by a *-endomorphism α, which depends not only on the pair (A,α) but also on the choice of a transfer operator (defined in the paper). With this we generalize some of the earlier constructions in the situations in which they behave best (e.g. for monomorphisms with hereditary range), but we get a different and perhaps more natural outcome in other situations. For example, we show that the Cuntz-Krieger algebra OA arises as the result of our construction when applied to the corresponding Markov subshift and a very natural transfer operator.