Complexes with the double centraliser property

TL;DR

This paper extends the double centraliser property from modules to complexes in derived categories of finite-dimensional algebras, providing characterizations and classifications, especially for hereditary and lower triangular matrix algebras.

Contribution

It introduces the derived double centraliser property for complexes and characterizes it, including classifications for specific algebra types.

Findings

Characterization of complexes with the derived double centraliser property

Classification of such complexes in derived categories of lower triangular matrix algebras

Identification of conditions for two-sided tilting complexes

Abstract

In representation theory, the double centraliser property is an important property for a module (bimodule). It plays a fundamental role in many theories. In this paper, we extend this property to complexes in derived categories of finite dimensional algebras, under the name derived double centraliser property. Characterizations for complexes with the derived double centraliser property and (two-sided) tilting complexes in derived categories of hereditary algebras are given. In particular, all complexes with this property in the derived categories of lower triangular matrix algebras are classified.