Related papers: Cluster tilting modules for local algebras
Let $A$ be a finite dimensional representation-finite algebra over an algebraically closed field. The aim of this work is to generalize the results proven in CGS. Precisely, we determine which vertices of $Q_A$ are sufficient to be…
We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation-finite algebra,…
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…
We introduce a relative tilting theory in abelian categories and show that this work offers a unified framework of different previous notions of tilting, ranging from Auslander-Solberg relative tilting modules on Artin algebras to…
(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting…
For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called…
We give an explicit description of the mutation classes of quivers of type \tilde{A}_n. Furthermore, we provide a complete classification of cluster tilted algebras of type \tilde{A}_n up to derived equivalence. We show that the bounded…
Let $Q$ be a finite acyclic quiver and $A_Q$ the cluster algebra of $Q$. It is well-known that for each field $k$, the additive equivalence classes of support tilting $kQ$-modules correspond bijectively with the clusters of $A_Q$. The aim…
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…
We construct two functors from the submodule category of a self-injective representation-finite algebra $\Lambda$ to the module category of the stable Auslander algebra of $\Lambda$. These functors factor through the module category of the…
For any truncated path algebra $\Lambda$, we give a structural description of the modules in the categories ${\cal P}^{<\infty}(\Lambda\text{-mod})$ and ${\cal P}^{<\infty}(\Lambda\text{-Mod})$, consisting of the finitely generated (resp.…
Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scattering amplitudes in physics. In this paper, we apply the…
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].
A cluster tilted algebra is known to be gentle if and only if it is cluster tilted of Dynkin type $\bbA$ or Euclidean type $\tilde{\bbA}$. We classify all finite dimensional algebras which are derived equivalent to gentle cluster tilted…
Matrix mutation appears in the definition of cluster algebras of Fomin and Zelevinsky. We give a representation theoretic interpretation of matrix mutation, using tilting theory in cluster categories of hereditary algebras. Using this, we…
A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…
Let ${\rm SI}_\beta(Q)$ be the semi-invariant ring of $\beta$-dimensional representations of a quiver $Q$. Suppose that $(Q,\beta)$ projects to another quiver with dimension vector $(Q',\beta')$ through an exceptional representation $E$. We…
We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization (in the sense of Schofield) of R at a set of finitely presented modules of projective dimension one. We…
We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of…
In this paper we describe all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an…