Support τ-tilting modules and semibricks over group graded algebras

Abstract

We consider a finite dimensional strongly G-graded algebra A with self-injective 1-component B, and in our main result we prove that the induction from B to A of a basic support τ-tilting pair of B-modules is a support τ-tilting pair (M,P) of A-modules if and only if M is G-invariant. A similar statement holds for the restriction from A to B, so our results may be viewed as Clifford and Maschke type theorems for 2-term silting complexes. We also give applications to semibricks and the associated wide subcategories.