On induced modules of inertial-invariant support $\tau$-tilting modules over blocks of finite groups

TL;DR

This paper proves that inducing support τ-tilting modules over certain finite group blocks preserves their support τ-tilting property, expanding understanding of module induction in representation theory.

Contribution

It establishes that induced modules of inertial-invariant support τ-tilting modules remain support τ-tilting, a novel result in the representation theory of finite groups.

Findings

Induced modules of inertial-invariant support τ-tilting modules are also support τ-tilting.

Supports the stability of τ-tilting properties under induction in specific group blocks.

Advances the theoretical framework of τ-tilting modules in modular representation theory.

Abstract

In this article, we prove that induced modules of support $\tau$-tilting modules over blocks of finite groups satisfying inertial-invariant condition are also support $\tau$-tilting modules.