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We consider C*-algebras of finite higher-rank graphs along with their rotational action. We show how the entropy theory of product systems with finite frames applies to identify the phase transitions of the dynamics. We compute the positive inverse temperatures where symmetry breaks, and in particular we identify the subharmonic parts of the gauge-invariant equilibrium states. Our analysis applies to positively weighted rotational actions through a recalibration of the entropies.
In this monograph we undertake a comprehensive study of separable representations (as well as their unitary equivalence classes) of $C^*$-algebras associated to strongly connected finite $k$-graphs $Lambda$. We begin with the representations associat
A higher rank numerical semigroup is a positive cone whose seminormalization is isomorphic to the free abelian semigroup. The corresponding nonselfadjoint semigroup algebras are known to provide examples that answer Arvesons Dilation Problem to the n
We introduce the notion of additive units, or `addits, of a pointed Arveson system, and demonstrate their usefulness through several applications. By a pointed Arveson system we mean a spatial Arveson system with a fixed normalised reference unit. We
In this paper we define the notion of monic representation for the $C^*$-algebras of finite higher-rank graphs with no sources, and undertake a comprehensive study of them. Monic representations are the representations that, when restricted to the co
We will define new constructions similar to the graph systems of correspondences described by Deaconu et al. We will use these to prove a version of Ionescus theorem for higher rank graphs. Afterwards we will examine the properties of these construct