Transfer of derived equivalences from subalgebras to endomorphism algebras

In this paper, we construct derived equivalences between subalgebras of some [Formula: see text]-Auslander–Yoneda algebras from a class of triangles in idempotent complete triangulated categories. The derived equivalences are obtained by transferring subalgebras induced by triangles to endomorphism algebras induced by approximation sequences.

On the Auslander-Yoneda Algebras of Modules over K[x]/(xn)

In the present paper we describe a class of Φ-Auslander-Yoneda algebras over K[x]/(xn) in terms of quivers with relations, and prove that they are actually cellular algebras in the sense of Graham and Lehrer.

ON THE EXISTENCE OF A DERIVED EQUIVALENCE BETWEEN A KOSZUL ALGEBRA AND ITS YONEDA ALGEBRA

In this paper, we study the derived categories of a Koszul algebra and its Yoneda algebra to determine when those categories are triangularly equivalent. We prove that the simply connected Koszul algebras are derived equivalent to their Yoneda algebras. We have considered discrete Koszul algebras and we gave necessary and sufficient conditions for those Koszul algebras to be derived equivalent to their Yoneda algebras. We also study the class of Koszul algebras which are derived equivalent to hereditary algebras. For the case where the hereditary algebra is tame, we characterized the derived equivalence between those Koszul algebras and their Yoneda algebras.

Derived equivalences from cohomological approximations and mutations of Φ-Yoneda algebras

A new construction of derived equivalences is given, which relates different endomorphism rings and, more generally, cohomological endomorphism rings, including higher extensions, of objects in triangulated categories. These objects need to be connected by certain universal maps that are cohomological approximations and that exist in very general circumstances. The construction turns out to be applicable to a wide variety of situations, covering finite-dimensional algebras as well as certain infinite-dimensional algebras, Frobenius categories and n-Calabi–Yau categories.