Related papers: The Self-injective Cluster Tilted Algebras
We give a complete description of all special biserial cluster-tilted algebras over a finite dimensional hereditary algebra H over an algebraically closed field K.
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
We compute the Hochschild cohomology groups of the cluster-tilted algebras of finite representation type.
We show how a cluster-tilted algebra of finite representation type is related to the corresponding tilted algebra, in the case of algebras defined over an algebraically closed field.
Let B be a cluster-tilted algebra. We prove that B is $\tau$-tilting finite if and only if B is representation-finite.
We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation…
We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type.
In this paper, we use the stable categories of some selfinjective algebras to describe the singularity categories of the cluster-tilted algebras of Dynkin type. Furthermore, in this way, we settle the problem of singularity equivalence…
We survey recent development of the study of finite-dimensional selfinjective algebras over a field which are socle equivalent to selfinjective orbit algebras of tilted type.
Cluster-tilted algebras are trivial extensions of tilted algebras. This correspondence induces a surjective map from tilted algebras to cluster-tilted algebras. If B is a cluster-tilted algebra, we use the fibre of B under this map to study…
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
In this paper, we characterize all the finite dimensional algebras that are derived equivalent to an m-cluster tilted algebra of type A tilde. This generalizes a result of Bobonski and Buan [9].
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…
We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\widetilde{A}$, using the geometric realization, we…
The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type $A_n$, by counting the mutation class of any quiver with underlying graph $A_n$. It will also follow that if $T$ and…
We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additionally, we classify the singularities of cluster algebras for…
We classify all finite dimensional algebras which are derived equivalent to m-cluster tilted algebras of type A.
Let k be a field. A finite dimensional k-algebra is said to be minimal representation-infinite provided it is representation-infinite and all its proper factor algebras are representation-finite. Our aim is to classify the special biserial…
In this paper, we introduce the notion of $\nu$-stable silting-discrete algebras, which unify silting-discrete algebras and tilting-discrete self-injective algebras, where $\nu$ is a triangle auto-equivalence of the bounded homotopy…
It is well known that the relation-extensions of tilted algebras are cluster-tilted algebras. In this paper, we extend the result to silted algebras and prove some extension of silted algebras are cluster-tilted algebras.