Related papers: Ideals in transformation-group $C^*$-algebras

In the present article we review an approximation procedure for amenable traces on unital and separable C*-algebras acting on a Hilbert space in terms of F\o lner sequences of non-zero finite rank projections. We apply this method to…

We study the link between stably finiteness and stably projectionless-ness for $C^*$-algebras of solvable Lie groups. We show that these two properties are equivalent if the dimension of the group is not divisible by $4$; otherwise, they…

We define "tracial" analogs of the Rokhlin property for actions of finite groups, approximate representability of actions of finite abelian groups, and of approximate innerness. We prove four analogs of related "nontracial" results. First,…

In this article we study the Golod property of standard graded algebras. We show that determinantal ideals, binomial edge ideals, and permanental ideals are Golod if and only if they have a linear resolution. Next, we give a…

Main result: If a C*-algebra is simple, $\sigma$-unital, has finitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier also has strict comparison of positive elements by traces. The same…

We define the profinite completion of a C*-algebra, which is a pro-C*-algebra, as well as the pro-C*-algebra of a profinite group. We show that the continuous representations of the pro-C*-algebra of a profinite group correspond to the…

We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full…

A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this…

In this paper, we describe primitive ideal space of the $C^*$-algebra $C^*(\Lambda)$ associated to any locally convex row-finite $k$-graph $\Lambda$. To do this, we will apply the Farthing's desourcifying method on a recent result of…

We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category $\mathcal{C}$ over a local ring…

We characterize the class of ideals of a polynomial ring such that the hilbert series of their graded local cohomology modules is maximal.

We show that the following properties of unital ${\rm C^*}$-algebra in a class of $\Omega$ are preserved by unital simple ${\rm C^*}$-algebra in the class of $\rm WTA\Omega$: $(1)$ uniform property $\Gamma$, $(2)$ a certain type of tracial…

We present a classification theorem for amenable simple stably projectionless C*-algebras with generalized tracial rank one whose $K_0$ vanish on traces which satisfy the Universal Coefficient Theorem. One of them is denoted by ${\cal Z}_0$…

The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal $I$ satisfying certain residual conditions, showing that ${\rm core}(I)$…

We study the topology of the primitive ideal space of groupoid C*-algebras for groupoids with abelian isotropy. Our results include the known results for action groupoids with abelian stabilizers. Furthermore, we obtain complete results…

We enlarge the class of $C^*$-algebras of Boolean dynamical systems in order to include all weakly left-resolving normal labelled space $C^*$-algebras in it. We prove a gauge-invariant uniqueness theorem and classify all gauge-invariant…

Let $M$ be a maximal subalgebra of a Lie algebra $L$ and $A/B$ a chief factor of $L$ such that $B \subseteq M$ and $A \not \subseteq M$. We call the factor algebra $M \cap A/B$ a $c$-section of $M$. All such $c$-sections are isomorphic, and…

Following Elliott's earlier work, we show that the Elliott invariant of any finite separable simple $C^*$-algebra with finite nuclear dimension can always be described as a scaled simple ordered group pairing together with a countable…

Given a partial action of a discrete group $G$ on a Hausdorff, locally compact, totally disconnected topological space $X$, we consider the correponding partial action of $G$ on the algebra $L_c(X)$ consisting of all locally constant,…

In this paper, we construct large subalgebras of crossed product C*-algebras of noncommutative C*-dynamics from ideals. We apply our results to study locally trivial unital $C(X)$-algebras such as mapping tori.