Indecomposable linear representation
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
This article gives a basic definition in the following area: linear representation theory
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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).
Note that in general, the property of being indecomposable is weaker than the property of being irreducible. But Maschke's theorem tells us that for a finite group and for a field whose characteristic does not divide the order of the group, every indecomposable representation is indeed irreducible.