相关论文: Rigidity of tilting complexes and derived equivale…

We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, also a complete stable equivalence classification of…

We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…

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.

By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…

The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an…

We prove that any derived equivalence between derived discrete algebras is standard, i.e.\ is isomorphic to the derived tensor product by a two-sided tilting complex.

We construct derived equivalences between group graded self-injective algebras, starting from equivalences between their 1-components, obtained via a construction of J. Rickard and S. Al-Nofayee.

We give a complete description of the derived equivalence normal forms of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings. As a consequence, a description of the…

We prove that any derived equivalence between derived-discrete algebras of finite global dimension is standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex.

We prove that a finite dimensional algebra is $\tau$-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a $\tau$-tilting finite algebra $A$ there is a bijection between isomorphism classes of…

The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categories, we study dominant dimensions of algebras under derived…

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 $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent…

We study tilting complexes over preprojective algebras of Dynkin type. We classify all tilting complexes by giving a bijection between tilting complexes and the braid group of the corresponding folded graph. In particular, we determine the…

To every minimal model of a complete local isolated cDV singularity Donovan--Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

We determine the structure of all finite-dimensional self-injective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice.

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle…

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…