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Interior product

In mathematics, the interior product (also known as interior derivative, interior multiplication, inner multiplication, inner derivative, insertion operator, contraction, or inner derivation) is a degree −1 (anti)derivation on the exterior algebra of differential forms on a smooth manifold. The interior product, named in opposition to the exterior…

Products, Cartan identity & Definition

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Cartan identity

Lie derivativeAnticommutatorSymplectic geometryGeneral relativityMomentum map
8 related topics

Definition

ContractionVector fieldManifoldMapAntiderivation
7 related topics

Properties

Exterior derivative
1 related topics

In Exterior Algebra

Hodge dual
1 related topics

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Definition

Properties

Cartan identity

In Exterior Algebra

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Interior product

Nodes31
Edges30
Triples15
Avg. degree1.94
Density0.064516
Components1

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Interior product

Top relations

related to Cartan identity · 6
Interior product → Cartan, Cartan's, Lie, The, The Cartan, This
related to Definition · 4
Interior product → Omega, The, Thus, When
related to In Exterior Algebra · 4
Interior product → Hodge, In, Similarly, The
is a · 1
Interior product → unique antiderivation of degree

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Important terminology

displaystyle interior product iota exterior vector contraction algebra derivative right omega also field left alpha inner identity wedge two derivation

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Interior productis aunique antiderivation of degree0.90text
Interior productrelated to Cartan identityThe0.60section
Interior productrelated to Cartan identityLie0.60section
Interior productrelated to Cartan identityCartan0.60section
Interior productrelated to Cartan identityThis0.60section
Interior productrelated to Cartan identityCartan's0.60section
Interior productrelated to Cartan identityThe Cartan0.60section
Interior productrelated to DefinitionThe0.60section
Interior productrelated to DefinitionThus0.60section
Interior productrelated to DefinitionOmega0.60section
Interior productrelated to DefinitionWhen0.60section
Interior productrelated to In Exterior AlgebraIn0.60section

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