Related papers: Regular ideals of graph algebras

Let $C^*(E)$ be the graph $C^*$-algebra associated to a graph E and let J be a gauge invariant ideal in $C^*(E)$. We compute the cyclic six-term exact sequence in $K$-theory of the associated extension in terms of the adjacency matrix…

We prove Leavitt path algebra versions of the two uniqueness theorems of graph C*-algebras. We use these uniqueness theorems to analyze the ideal structure of Leavitt path algebras and give necessary and sufficient conditions for their…

Let $\mathcal{G}$ be an ultragraph and let $C^*(\mathcal{G})$ be the associated $C^*$-algebra introduced by Mark Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*(\mathcal{G})$, we approach the quotient $C^*$-algebra…

Given a topological graph $E$, we give a complete description of tracial states on the C*-algebra $\mathrm{C}^*(E)$ which are invariant under the gauge action; there is an affine homeomorphism between the space of gauge invariant tracial…

We describe the primitive ideal space of the $C^{\ast}$-algebra of a row-finite $k$-graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces can occur, and compute the primitive ideal space of two…

We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.

We prove a sandwiching lemma for inner-exact locally compact Hausdorff \'etale groupoids. Our lemma says that every ideal of the reduced $C^*$-algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined…

Let $\mathcal{G}$ be an ultragraph and let $C^*(\mathcal{G})$ be the associated $C^*$-algebra introduced by Mark Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*(\mathcal{G})$, we analyze the structure of the quotient…

We address the classification problem for graph $C^*$-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that…

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each vertex in G can be reached by an infinite…

Let $(G, \Lambda)$ be a self-similar $k$-graph with a possibly infinite vertex set $\Lambda^0$. We associate a universal C*-algebra $\mathcal{O}_{G,\Lambda}$ to $(G,\Lambda)$. The main purpose of this paper is to investigate the ideal…

To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to…

Various questions on Lie ideals of C*-algebras are investigated. They fall roughly under the following topics: relation of Lie ideals to closed two-sided ideals; Lie ideals spanned by special classes of elements such as commutators,…

If $I$ is a (two-sided) ideal of a ring $R$, we let $\operatorname{ann}_l(I)=\{r\in R\mid rI=0\},$ $\operatorname{ann}_r(I)=\{r\in R\mid Ir=0\},$ and $\operatorname{ann}(I)=\operatorname{ann}_l(I)\cap \operatorname{ann}_r(I)$ be the left,…

We initiate the study of C*-algebras and groupoids arising from left regular representations of Garside categories, a notion which originated from the study of Braid groups. Every higher rank graph is a Garside category in a natural way. We…

We investigate conditions on a graph $C^*$-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth $(1,\infty)$-summable semfinite…

A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of $L$ contained in B. This is analogous to the concept of c-normal subgroup,…

We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the…

We describe primitive and prime ideals in the C*-algebra C*(E) of a graph E satisfying Condition (K), together with the topologies on each of these spaces. In particular, we find that primitive ideals correspond to the set of maximal tails…

We study $C^*$-algebras arising from $C^*$-correspondences, which was introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our $C^*$-algebras to be nuclear, exact, or satisfy the Universal…