相关论文: Silting correspondences and Calabi-Yau dg algebras
Assume that $\D$ is a Krull-Schmidt, Hom-finite triangulated category with a Serre functor and a cluster-tilting object $T$. We introduce the notion of relative cluster tilting objects, and $T[1]$-cluster tilting objects in $\D$, which are…
We give a structure theorem for Calabi-Yau triangulated category with a hereditary cluster tilting object. We prove that an algebraic $d$-Calabi-Yau triangulated category with a $d$-cluster tilting object $T$ such that its shifted sum…
We show that a tilting module over the endomorphism algebra of a cluster-tilting object in a 2-Calabi-Yau triangulated category lifts to a cluster-tilting object in this 2-Calabi-Yau triangulated category. This generalizes a recent work of…
We establish a bijective correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures of $\mathsf{D}_{\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more…
We study higher cluster tilting objects in generalized higher cluster categories arising from dg algebras of higher Calabi-Yau dimension. Taking advantage of silting mutations of Aihara-Iyama, we obtain a class of $m$-cluster tilting…
It is shown that the silting reduction $\ct/\thick\cp$ of a triangulated category $\ct$ with respect to a presilting subcategory $\cp$ can be realized as a certain subfactor category of $\ct$, and that there is a one-to-one correspondence…
We prove the existence of an $m$-cluster tilting object in a generalized $m$-cluster category which is $(m+1)$-Calabi-Yau and Hom-finite, arising from an $(m+2)$-Calabi-Yau dg algebra. This is a generalization of the result for the ${m =…
For a finite-dimensional algebra $\Lambda$ over an algebraically closed field $K$, it is known that the poset of $2$-term silting objects in $\mathrm{K}^b(\operatorname{proj}\Lambda)$ is isomorphic to the poset of functorially finite…
In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this…
We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection…
Let $U$ be a silting object in a derived category over a dg-algebra $A$, and let $B$ be the endomorphism dg-algebra of $U$. Under some appropriate hypotheses, we show that if $U$ is good, then there exist a dg-algebra $C$, a homological…
We construct the intermediate coverings of cluster-tilted algebras by defining the generalized cluster categories. These generalized cluster categories are Calabi-Yau triangulated categories with fraction CY-dimension and have also cluster…
We introduce a notion of global dimension for a triangulated category relative to a compact silting object. We prove that the finiteness of this dimension is an intrinsic property of the triangulated category itself and, therefore,…
We investigate cluster tilting objects (and subcategories) in triangulated 2-Calabi-Yau categories and related categories. In particular we construct a new class of such categories related to preprojective algebras of non Dynkin quivers…
We provide an explicit procedure to glue (not necessarily compact) silting objects along recollements of triangulated categories with coproducts having a 'nice' set of generators, namely, well generated triangulated categories. This…
A triangulated category is said to be Calabi-Yau of dimension d if the dth power of its suspension is a Serre functor. We determine which stable categories of self-injective algebras A of finite representation type are Calabi-Yau and…
As a generalization of acyclic 2-Calabi-Yau categories, we consider 2-Calabi-Yau categories with a directed cluster-tilting subcategory; we study their cluster-tilting subcategories and the cluster combinatorics that they encode. We show…
We introduce the notion of ST-pairs of triangulated subcategories, a prototypical example of which is the pair of the bound homotopy category and the bound derived category of a finite-dimensional algebra. For an ST-pair $(\C,\D)$, we…
We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of $d$-cluster tilting modules over $d$-representation-finite algebras. This is an application of…
The aim of this paper is to introduce tau-tilting theory, which completes (classical) tilting theory from the viewpoint of mutation. It is well-known in tilting theory that an almost complete tilting module for any finite dimensional…