10 citations · 35 across the 12 of their papers we have counts for
10 papers · 1 filter
Groupoid homology and K-theory for algebraic actions from number theory
Chris Bruce, Yosuke Kubota, Takuya Takeishi
We compute the groupoid homology for the ample groupoids associated with algebraic actions from rings of algebraic integers and integral dynamics. We derive results for the homolog…
A tracial characterization of Furstenberg's conjecture
Chris Bruce, Eduardo Scarparo
We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers and , we show that Fursten…
On the C*-algebra associated with the full adele ring of a number field
Chris Bruce, Takuya Takeishi
The multiplicative group of a number field acts by multiplication on the full adele ring of the field. Generalising a theorem of Laca and Raeburn, we explicitly describe the primit…
Algebraic actions I. C*-algebras and groupoids
Chris Bruce, Xin Li
We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce…
Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras
Chris Bruce, Takuya Takeishi
We prove that the class of crossed product C*-algebras associated with the action of the multiplicative group of a number field on its ring of finite adeles is rigid in the followi…
C*-dynamical invariants and Toeplitz algebras of graphs
Chris Bruce, Takuya Takeishi
In recent joint work of the authors with Laca, we precisely formulated the notion of partition function in the context of C*-dynamical systems. Here, we compute the partition funct…
Partition functions as C*-dynamical invariants and actions of congruence monoids
Chris Bruce, Marcelo Laca, Takuya Takeishi
We study the phase transition of KMS states for the C*-algebras of -semigroups of algebraic integers in which the multiplicative part is restricted to a congruence monoid, as…
On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoids
Chris Bruce, Xin Li
We study semigroup C*-algebras of semigroups associated with number fields and initial data arising naturally from class field theory. Using K-theoretic invariants, we investigate…
Phase transitions on C*-algebras from actions of congruence monoids on rings of algebraic integers
Chris Bruce
We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $β\…
Equilibrium states and growth of quasi-lattice ordered monoids
Chris Bruce, Marcelo Laca, Jacqui Ramagge +1
Each multiplicative real-valued homomorphism on a quasi-lattice ordered monoid gives rise to a quasi-periodic dynamics on the associated Toeplitz C*-algebra; here we study the KMS…