Crossed-Products by Finite Index Endomorphisms and KMS states
| dc.creator | Exel, Ruy | |
| dc.date | 2001-05-24 | |
| dc.date.accessioned | 2026-07-07T04:41:50Z | |
| dc.date.available | 2026-07-07T04:41:50Z | |
| dc.description | 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^{-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.description | Plain TeX, 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0105195 | |
| dc.identifier | http://arxiv.org/abs/math/0105195 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61524 | |
| dc.subject | Operator Algebras | |
| dc.subject | Mathematical Physics | |
| dc.subject | Dynamical Systems | |
| dc.subject | 46L55 | |
| dc.title | Crossed-Products by Finite Index Endomorphisms and KMS states | |
| dc.type | text |