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Semisimple representation

In mathematics, specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation of a group or an algebra that is a direct sum of simple representations (also called irreducible representations). It is an example of the general mathematical notion of semisimplicity.

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Overview

Equivalent characterizations

Examples and non-examples

Semisimple decomposition and multiplicity

Isotypic decomposition

Completion

Applications to physics

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Map overview Semantic statistics

Semisimple representation

Nodes87
Edges86
Triples31
Avg. degree1.98
Density0.022989
Components1

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Semisimple representation

Top relations

related to Completion · 10
Semisimple representation → As, Fourier, Hilbert, Hilbert-space, In, In Fourier, Note, Peter, The, Weyl
related to Unitary representations · 6
Semisimple representation → For, G-invariant, GL, Hence, Maschke's, Such
related to Semisimple decomposition and multiplicity · 5
Semisimple representation → By, However, Schur's, Suppose, The
related to Associated semisimple representation · 4
Semisimple representation → Given, Hölder, Jordan, Then
related to Equivalent characterizations · 3
Semisimple representation → In, Let, The
related to Isotypic decomposition · 3
Semisimple representation → By, Then, There

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Important terminology

displaystyle representation semisimple simple group representations sum direct operatorname algebra decomposition finite-dimensional example subrepresentation oplus irreducible space ker cap isotypic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Semisimple representationrelated to Associated semisimple representationGiven0.60section
Semisimple representationrelated to Associated semisimple representationJordan0.60section
Semisimple representationrelated to Associated semisimple representationHölder0.60section
Semisimple representationrelated to Associated semisimple representationThen0.60section
Semisimple representationrelated to CompletionIn Fourier0.60section
Semisimple representationrelated to CompletionFourier0.60section
Semisimple representationrelated to CompletionIn0.60section
Semisimple representationrelated to CompletionThe0.60section
Semisimple representationrelated to CompletionPeter0.60section
Semisimple representationrelated to CompletionWeyl0.60section
Semisimple representationrelated to CompletionHilbert-space0.60section
Semisimple representationrelated to CompletionAs0.60section

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