Related papers: On cluster C*-algebras

Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the cluster category. Any cluster of the cluster algebra corresponds…

We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C*-correspondences and Cuntz-Pimsner algebras. We show that the C*-algebra…

We apply the abelianization technique to obtain an explicit ring presentation for the quasimap quantum cohomology of GIT quotients. As an application, for quiver varieties associated with oriented-acyclic quivers, we establish a cluster…

Let $G$ be a locally compact group with cocompact connected component. We prove that the assembly map from the topological $\k$-theory of $G$ to the $\k$-theory of the reduced $C^*$-algebra of $G$ is an isomorphism.

This survey article on relative homological algebra in bivariant K-thoery is mainly intended for readers with a background knowledge in triangulated categories. We briefly recall the general theory of relative homological algebra in…

A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…

We provide a complete classification of the singularities of cluster algebras of finite type with trivial coefficients. Alongside, we develop a constructive desingularization of these singularities via blowups in regular centers over fields…

We define the cluster algebra associated with the Q-system for the Kirillov-Reshetikhin characters of the quantum affine algebra $U_q(\hat{\g})$ for any simple Lie algebra g, generalizing the simply-laced case treated in [Kedem 2007]. We…

We describe a new way to relate an acyclic, skew-symmetrizable cluster algebra to the representation theory of a finite dimensional hereditary algebra. This approach is designed to explain the c-vectors of the cluster algebra. We obtain a…

We consider a quiver $Q$ of ADE type and use cluster combinatorics to define two complex manifolds $\mathcal S$ and $\mathcal L$. The space $\mathcal S$ can be identified with a quotient of the space of stability conditions on the CY$_3$…

Let $Q$ be an acyclic quiver. Associated with any element $w$ of the Coxeter group of $Q$, triangulated categories $\underline{\Sub}\Lambda_w$ were introduced in \cite{Bua2}. There are shown to be triangle equivalent to generalized cluster…

We study non-commutative algebraic geometry of Artin, Serre and Tate in terms of the operator algebras. Namely, we define the Serre $C^*$-algebra $\mathcal{A}_X$ of a projective variety $X$ as the norm-closure of a representation of the…

In this paper we study the derived equivalences between surface algebras, introduced by David-Roesler and Schiffler. Each surface algebra arises from a cut of an ideal triangulation of an unpunctured marked Riemann surface with boundary. A…

We prove that the Cuntz-Pimsner algebra O(E) of a vector bundle E over a compact metrizable space X is determined up to an isomorphism of C(X)-algebras by the ideal (1-[E])K(X) of the K-theory ring K(X). Moreover, if E and F are vector…

In \cite{rupel3},the authors defined algebra homomorphisms from the dual Ringel-Hall algebra of certain hereditary abelian category $\mathcal{A}$ to an appropriate $q$-polynomial algebra. In the case that $\mathcal{A}$ is the representation…

We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups $S$ and $T$, there is another Cuntz semigroup $[[S,T]]$ playing the role of morphisms from $S$ to $T$. Applied to C$^*$-algebras…

Let $X$ be an infinite compact metrizable space, and let $\sigma: X\to X$ be a minimal homeomorphism. Suppose that $(X, \sigma)$ has zero mean topological dimension. The associated C*-algebra $A=\mathrm{C}(X)\rtimes_\sigma\mathbb Z$ is…

Let $Q$ be a finite quiver without oriented cycles and $k$ an algebraically closed field.In this paper we establish a connection between cluster algebras and the representation theory of the path algebra $kQ$, in terms of the spectral…

The article concerns the subalgebra U_v^+(w) of the quantized universal enveloping algebra of the complex Lie algebra sl_{n+1} associated with a particular Weyl group element of length 2n. We verify that U_v^+(w) can be endowed with the…

The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects $T$ in cluster categories; we call such an algebra cluster-concealed in case $T$ is obtained from a…