Related papers: On tilting modules over cluster-tilted algebras

Tilting modules, generalising the notion of progenerator, furnish equivalences between pieces of module categories. This paper is dedicated to study how much these pieces say about the whole category. We will survey the existing results in…

Let $T$ be an infinitely generated tilting module of projective dimension at most one over an arbitrary associative ring $A$, and let $B$ be the endomorphism ring of $T$. In this paper, we prove that if $T$ is good then there exists a ring…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

Let $\mathcal{C}$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster tilting object. Under some constructibility assumptions on $\mathcal{C}$ which are satisfied for instance by cluster categories, by generalized cluster…

In the present paper the cyclic homology functor from the category of $A_\infty$-algebras over any commutative unital ring $K$ to the category of graded $K$-modules is constructed. Further, it is showed that this functor sends homotopy…

Tilting modules over commutative rings were recently classified in [12]: they correspond bijectively to faithful Gabriel topologies of finite type. In this note we extend this classification by dropping faithfulness. The counterpart of an…

In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra of euclidean type, we define the notion of reflection so…

We show that the category of finite-dimensional modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category is equivalent to the Gabriel-Zisman localisation of the category with respect to a certain class…

We use the category of linear complexes of tilting modules for the BGG category O, associated with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic way several known results about O obtained earlier by…

Following the previous work, we determine exactly the highest weights for which a tensor product of two induced modules is a tilting module, for the algebraic group $SL_2$ over an algebraically closed field of positive characteristic.

In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for…

We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise…

We define mutation on coloured quivers associated to tilting objects in higher cluster categories. We show that this operation is compatible with the mutation operation on the tilting objects. This gives a combinatorial approach to tilting…

Recent results by Keller and Nicol{\'a}s and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other…

Let $G=SL(2,5)$ be the special linear group of $2 \times 2$-matrices with coefficients in the field with $5$ elements. We show that the principal block over a splitting field $K$ of characteristic two of the group algebra $KG$ has a…

Let $\mathcal{H}$ be a connected hereditary abelian category with tilting objects. It is proved that the cluster-tilting graph associated with $\mathcal{H}$ is always connected. As a consequence, we establish the connectedness of the…

Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field $k$ and $\mathscr{C}_{F^m}$ be the repetitive cluster category of $H$ with $m\geq 1$. We investigate the properties of cluster tilting objects in…

Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then…

In representation theory of algebras the notion of `mutation' often plays important roles, and two cases are well known, i.e. `cluster tilting mutation' and `exceptional mutation'. In this paper we focus on `tilting mutation', which has a…

For any good tilting module $T$ over a ring $A$, there exists an $n$-symmetric subcategory $\mathscr{E}$ of a module category such that the derived category of the endomorphism ring of $T$ is a recollement of the derived categories of…