Derived equivalences for a class of PI algebras

TL;DR

This paper characterizes tilting complexes for a class of PI algebras with prime spectra homeomorphic to their centers, showing derived equivalences imply Morita equivalences for these algebras.

Contribution

It provides a description of tilting complexes for certain PI algebras and proves that derived equivalence implies Morita equivalence within this class.

Findings

Derived equivalences imply Morita equivalences for the considered PI algebras.

A classification of tilting complexes for these algebras.

Application to Sklyanin algebras.

Abstract

A description of tilting complexes is given for a class of PI algebras whose prime spectrum is canonically homeomorphic to the prime spectrum of its center. Some Sklyanin algebras are the kind of algebras considered. As an application, it is proved that any algebra derived equivalent to such kind of algebra, is Morita equivalent to it.