Semilinear tensor decompositions

Abstract

We prove that a kG-module has a semilinear tensor decomposition if and only if its endomorphism algebra has a pair of mutually centralizing, unital, G-invariant subalgebras that are not commutative and are isomorphic to complete matrix algebras over an extension field K of k. We give an algorithm that constructs a semilinear tensor decomposition for any module whose endomorphism algebra contains appropriate invariant subalgebras.