2001/05/24 by Ruy Exel, Exel, Ruy
Mathematics · Physics and Astronomy · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.DS #math.MP #math.OA #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/0105195
Plain TeX, 24 pages
arxiv created 2001/05/24 · openalex publication_date 2001/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a unital C*-algebra A, an injective endomorphism α:A --> A preserving the unit, and a conditional expectation E from A to the range of αwe consider the crossed-product of A by αrelative to the transfer operator L=α-1E. When E is of index-finite type we show that there exists a conditional expectation G from the crossed-product to A which is unique under certain hypothesis. We define a "gauge action" on the crossed-product algebra in terms of a central positive element h and study its KMS states. The main result is: if h>1 and E(ab)=E(ba) for all a,b in A (e.g. when A is commutative) then the KMSβstates are precisely those of the form ψ= ϕG, where ϕis a trace on A satisfying the identity ϕ(a) = ϕ(L(h-βind(E)a)), where ind(E) is the Jones-Kosaki-Watatani index of E.