Which canonical algebras are derived equivalent to incidence algebras of posets?

TL;DR

This paper classifies canonical algebras over algebraically closed fields that are derived equivalent to incidence algebras of finite posets, focusing on those with two or three weights.

Contribution

It provides a complete characterization of canonical algebras derived equivalent to incidence algebras of finite posets, specifically those with 2 or 3 weights.

Findings

Canonical algebras with 2 weights are derived equivalent to certain incidence algebras.

Canonical algebras with 3 weights are also classified in terms of derived equivalence.

No other canonical algebras with more than 3 weights are derived equivalent to incidence algebras.

Abstract

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras whose number of weights is either 2 or 3.