Double Hall algebras and derived equivalences

TL;DR

This paper proves that the reduced Drinfeld double of the Ringel-Hall algebra remains unchanged under derived equivalences of hereditary categories, extending previous results with explicit isomorphisms.

Contribution

It establishes invariance of the reduced Drinfeld double under derived equivalences and provides explicit isomorphisms for these transformations.

Findings

Invariance of the reduced Drinfeld double under derived equivalences

Explicit isomorphisms associated with derived equivalences

Extension of previous results in the literature

Abstract

We show that the reduced Drinfeld double of the Ringel-Hall algebra of a hereditary category is invariant under derived equivalences. By associating an explicit isomorphism to a given derived equivalence, we also extend the results of [BS1], [BS2], [SVdB], and [XY].