Indecomposable linear representation: Difference between revisions
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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 [[subrepresentation]]s). | 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 [[subrepresentation]]s). | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Irreducible linear representation]] | |||
Revision as of 03:03, 27 August 2007
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).