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Irreducible representation

In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic structure A {\displaystyle A} is a nonzero representation that has no proper nontrivial subrepresentation ( ρ | W , W ) {\displaystyle (\rho |_{W},W)} , with W ⊂ V {\displaystyle…

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Overview

History

Examples of irreducible representations

Applications in theoretical physics and chemistry

Lie groups

Associative algebras

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Irreducible representation

Nodes72
Edges71
Triples72
Avg. degree1.97
Density0.027778
Components1

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Irreducible representation

Top relations

related to External links · 50
Irreducible representation → Answers, Archived, Bekaert, Beveren, Boulanger, Commission, Constantin, David, Dermisek, Eef, Emma, Feinberg, Finley, Groups, Guild, Hunt, IR, Joseph, Kyle, Lie Algebra
related to Connection between irreducible representation and indecomposable representation · 5
Irreducible representation → An, In, Maschke's, The, When
related to Example of an irreducible representation over Fp · 5
Irreducible representation → By Orbit-stabilizer, Let, Since, That, This
related to Irreducible complex representations · 5
Irreducible representation → All, In, Let, The, Then
has application · 4
Irreducible representation → Hamiltonian, Identifying, In, Thus
related to history · 3
Irreducible representation → Group, Richard Brauer, The

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Important terminology

displaystyle representation group representations irreducible pdf isbn theory quantum matrices matrix sum rho groups indecomposable mechanics space direct complex lorentz

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Irreducible representationhas applicationIn0.60section
Irreducible representationhas applicationHamiltonian0.60section
Irreducible representationhas applicationIdentifying0.60section
Irreducible representationhas applicationThus0.60section
Irreducible representationrelated to Connection between irreducible representation and indecomposable representationAn0.60section
Irreducible representationrelated to Connection between irreducible representation and indecomposable representationThe0.60section
Irreducible representationrelated to Connection between irreducible representation and indecomposable representationMaschke's0.60section
Irreducible representationrelated to Connection between irreducible representation and indecomposable representationWhen0.60section
Irreducible representationrelated to Connection between irreducible representation and indecomposable representationIn0.60section
Irreducible representationrelated to Example of an irreducible representation over FpLet0.60section
Irreducible representationrelated to Example of an irreducible representation over FpBy Orbit-stabilizer0.60section
Irreducible representationrelated to Example of an irreducible representation over FpSince0.60section

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