A characterization for induced modules to be support $\tau$-tilting modules

TL;DR

This paper establishes a precise criterion for when induced modules from a normal subgroup are support τ-tilting modules over group algebras, including a block version, advancing the understanding of module induction in representation theory.

Contribution

It provides a necessary and sufficient condition for induced modules to be support τ-tilting, extending the theory to block algebras.

Findings

Characterization criterion for support τ-tilting modules

Extension of results to block algebras

Enhanced understanding of module induction in group representation

Abstract

Let $\tilde{G}$ be a finite group and $G$ a normal subgroup of $\tilde{G}$. In this paper, we give a necessary and sufficient condition for $\mathrm{Ind}_G^{\tilde{G}}M$ to be a support $\tau$-tilting $k\tilde{G}$-module for a $kG$-module $M$. Moreover, we give the block version of the result.