Crossed-Products by Finite Index Endomorphisms and KMS states

dc.creatorExel, Ruy
dc.date2001-05-24
dc.date.accessioned2026-07-07T04:41:50Z
dc.date.available2026-07-07T04:41:50Z
dc.descriptionGiven 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^{-1}E. 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 KMS_βstates are precisely those of the form ψ= ϕG, where ϕis a trace on A satisfying the identity ϕ(a) = ϕ(L(h^{-β}ind(E)a)), where ind(E) is the Jones-Kosaki-Watatani index of E.
dc.descriptionPlain TeX, 24 pages
dc.identifierhttps://arxiv.org/abs/math/0105195
dc.identifierhttp://arxiv.org/abs/math/0105195
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61524
dc.subjectOperator Algebras
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subject46L55
dc.titleCrossed-Products by Finite Index Endomorphisms and KMS states
dc.typetext

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