Indecomposable linear representation

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This article describes a property to be evaluated for a linear representation of a group, i.e. a homomorphism from the group to the general linear group of a vector space over a field

Definition

Symbol-free definition

A linear representation of a group is said to be indecomposable if it cannot be expressed as a direct sum of linear representations with both summands being nonzero (or equivalently, it cannot be expressed as a direct sum of proper nonzero subrepresentations).

Relation with other properties

Stronger properties