Partial actions and KMS states on relative graph C⁎-algebras☆
By Toke Meier Carlsen, Nadia S. Larsen. 2013
51 citations recorded by the source corpus.
Abstract The relative graph C ⁎ -algebras introduced by Muhly and Tomforde are generalizations of both graph algebras and their Toeplitz extensions. For an arbitrary graph E and a subset R of the set of regular vertices of E we show that the relative graph C ⁎ -algebra C ⁎ ( E , R ) is isomorphic to a partial crossed product for an action of the free group generated by the edge set on the relative boundary path space. Given a time evolution on C ⁎ ( E , R ) induced by a function on the edge set, we characterize the KMS β states and ground states using an abstract result of Exel and Laca. Guided by their work on KMS states for Toeplitz–Cuntz–Krieger type algebras associated to infinite matrices, we obtain complete descriptions of the convex sets of KMS states of finite type and of KMS states of infinite type whose associated measures are supported on recurrent infinite paths. This allows us to give a complete concrete description of the convex set of all KMS states for a big class of graphs which includes all graphs with finitely many vertices.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8a66ae679bf2297652765458159893877f8f6487
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Recent developments around partial actions (2018, background): “ applied in [2] to the study of the ideal structure of full and reduced cross-sectional C∗-algebras of Fell bundles, in [25] to the investigation of C∗-algebras of dynamical systems of type (m,n), in [74] to relative graph C∗-algebras, in [118] to C∗-algebras associated to arbitrary subshifts, in [1”
- Infinite alphabet edge shift spaces via ultragraphs and their C*-algebras (2017, background): “ [1, 8]). Note that if t∈ F is not of the form t= ab−1, with a,b∈ P∪ {0F} then C(Xt) is the null ideal and αt is the null map. Remark 4.6 The partial action above coincides with the one introduced in [5] when G is a directed graph without sinks. To prove that the C*-algebra of an ultragraph G, C∗(G)”