Some Homological Properties of Tensor and Wreath Products of Quasi-hereditary Algebras

TL;DR

This paper investigates how certain homological properties of quasi-hereditary algebras are preserved when taking their wreath products with symmetric groups, revealing inheritance of duality, Koszulity, and Ext-algebra conditions.

Contribution

It demonstrates that wreath products of quasi-hereditary algebras retain key homological properties, extending understanding of their structural behavior.

Findings

Wreath product preserves BGG duality.

Standard Koszulity is inherited.

Ext-algebra of standard modules remains Koszul.

Abstract

We show that taking the wreath product of a quasi-hereditary algebra with symmetric group inherits several homological properties of the original algebra, namely BGG duality, standard Koszulity, balancedness as well as a condition which makes the Ext-algebra of its standard modules a Koszul algebra.