On $\tau$-tilting finiteness of block algebras of direct products of finite groups

TL;DR

This paper investigates the conditions under which tensor products of symmetric algebras, especially block algebras of direct products of finite groups, have finitely many $ au$-tilting modules, linking algebraic structure to module theory.

Contribution

It provides new criteria for $ au$-tilting finiteness in tensor products of symmetric algebras and applies these results to block algebras of direct product groups.

Findings

Criteria for $ au$-tilting finiteness established

Finiteness conditions applied to block algebras of finite groups

Insights into the structure of $ au$-tilting modules over tensor products

Abstract

We discuss finiteness/infiniteness of $\tau$-tilting modules over tensor products of two symmetric algebras. As an application, we discuss that over block algebras of direct products of finite groups.