KMS and Ground States on Ultragraph C*-Algebras

Continuous shift commuting maps between ultragraph shift spaces

“…In a similar way, in the finite alphabet case, a Markov shift is the spectrum of an abelian subalgebra of the associated Cuntz-Krieger algebra, see [4]. Although the theory of shift spaces defined in [12] is still in its infancy, there has been already applications to KMS states associated to ultragraph C*-algebras, see [2], and to the diagonal-preserving isomorphism problem of ultragraph C*-algebras, see [1,12].…”

KMS states and continuous orbit equivalence for ultragraph shift spaces with sinks

“…Once we have extended the definition of ultragraph shift spaces to include sinks, we provide further evidence that these shift spaces are well connected with C*-algebras, namely we describe continuous orbit equivalence of ultragraph shift spaces in terms of isomorphism of the associated groupoids and in terms of isomorphism of the associated C*-algebras. Furthermore, using partial crossed product theory, we study the dynamics associated with these shifts: we describe the KMS and ground states associated to ultragraph C*-algebras, extending results in [10] to include ultragraphs with sinks.…”

Li-Yorke Chaos for ultragraph shift spaces

“…Recently, Ott-Tomforde-Willis proposed a shift space connected with C*-algebras and many of its properties were studied (see [9,10,12,14,17]). Deepening the connection with C*-algebras, and building on work of Webster (see [24]), a new generalization of shifts of finite type to the infinite alphabet case was proposed in [8] (see [3] for further connections with C*-algebras). The definition in [8] relies on ultragraphs and the resulting shift space contains a countable basis of clopen subsets (which for ultragraphs that satisfy a mild condition turn to be compact-open subsets).…”