A note on standard equivalences

TL;DR

This paper proves that all derived equivalences between triangular algebras are standard, meaning they can be represented by derived tensor functors from two-sided tilting complexes.

Contribution

It establishes that any derived equivalence between triangular algebras is isomorphic to a standard derived tensor functor, confirming a key structural property.

Findings

All derived equivalences between triangular algebras are standard.

Derived equivalences are isomorphic to tensor functors from two-sided tilting complexes.

The result simplifies understanding of derived equivalences in this class of algebras.

Abstract

We prove that any derived equivalence between triangular algebras is standard, that is, it is isomorphic to the derived tensor functor given by a two-sided tilting complex.