KMS STATES ON THE C -ALGEBRAS OF NON-PRINCIPAL GROUPOIDS

By Sergey Neshveyev. 2011

73 citations recorded by the source corpus.

We describe KMS-states on the C -algebras of etale groupoids in terms of measurable elds of traces on the C -algebras of the isotropy groups. We use this description to analyze tracial states on the transformation groupoid C -algebras and to give a short proof of recent results of Cuntz, Deninger and Laca on the Toeplitz algebras of the ax +b semigroups of the rings of integers in number elds.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/76a5950a69b515cabb1d7772da9d1dcc88dbe1d4

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

KMS states on the C∗-algebras of finite graphs (2012, methodology): “k,z) = z. The sets Z(α,γ) := {(αy,|γ|− |α|,γy) : y∈ G(0),s(α) = s(γ) = r(y)} form a basis of compact-open sets for the topology on G. When we view T C∗(E) as C∗(G), our dynamics is the one studied in [14] for the cocycle c: G→ R deﬁned by c(y,k,z) = k. To construct KMS states on C∗(G) using Neshveye”
Partial actions and KMS states on relative graph C⁎-algebras☆ (2013, background): “1 can be seen in relation to the general result for groupoid algebras in [22] because the C∗-algebra C∗(E,R) admits a realization as a groupoid C∗-algebra C(G(E,R)) where G := G(E,R) = {(ux, |u| − |u ′|, u′x) | u, u′ ∈ E∗, x ∈ ∂RE, r(u) = s(x) = r(u ′)}, see for example [23] and [13, §6.”