Blockwise relations between triples, and derived equivalences for wreath products

TL;DR

This paper explores how blockwise relations between module triples relate to derived equivalences and demonstrates their compatibility with wreath products, advancing understanding in local-global conjectures.

Contribution

It establishes that blockwise relations are consequences of derived equivalences with specific properties and shows their compatibility with wreath products.

Findings

Blockwise relations follow from derived equivalences with extra properties.

Relations are compatible with wreath product constructions.

Advances understanding of local-global conjectures in representation theory.

Abstract

Motivated by the reduction techniques involving character triples for the local-global conjectures, we show that a blockwise relation between module triples is a consequence of a derived equivalence with additional properties. Moreover, we show that this relation is compatible with wreath products.