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Super vector space

In mathematics, a super vector space is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded vector space, that is, a vector space over a field K {\displaystyle \mathbb {K} } with a given decomposition of subspaces of grade 0 {\displaystyle 0} and grade 1 {\displaystyle 1} . The study of super vector spaces and their generalizations is sometimes called super…

Products, The category of super vector spaces & Linear transformations

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The category of super vector spaces

ObjectsCategory theorySuperalgebrasLie superalgebrasSupergroups
10 related topics

Linear transformations

HomomorphismMorphismCategoryLinear transformationIsomorphism
6 related topics

Supermodules

ModulesCommutative ringSupermodulesSupercommutative algebraGrassmann algebra
6 related topics

Operations on super vector spaces

Dual spaceFunctionalsDirect sumsTensor products
4 related topics

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Overview

Definitions

Linear transformations

Operations on super vector spaces

Supermodules

The category of super vector spaces

Superalgebra

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Map overview Semantic statistics

Super vector space

Nodes47
Edges46
Triples24
Avg. degree1.96
Density0.042553
Components1

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Super vector space

Top relations

related to Linear transformations · 4
Super vector space → An, Hom, That, The
related to Tensor product · 4
Super vector space → Here, One, Specifically, The
related to The category of super vector spaces · 4
Super vector space → Lie, SVect, The, This
related to Supermodules · 3
Super vector space → Given, Grassmann, Just
is a · 2
Super vector space → linear subspace that is spanned by homogeneous elements, Z 2
related to Definitions · 2
Super vector space → The, Vectors
related to Dual space · 2
Super vector space → Equivalently, The
related to Direct sum · 1
Super vector space → Direct
related to Operations on super vector spaces · 1
Super vector space → The
related to Superalgebra · 1
Super vector space → This

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Important terminology

super vector displaystyle space spaces mathbb linear even category given odd elements mathrm field one algebra homogeneous svect homomorphism denoted

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Super vector spaceis aZ 20.90text
Super vector spaceis alinear subspace that is spanned by homogeneous elements0.90text
Super vector spacerelated to DefinitionsVectors0.60section
Super vector spacerelated to DefinitionsThe0.60section
Super vector spacerelated to Direct sumDirect0.60section
Super vector spacerelated to Dual spaceThe0.60section
Super vector spacerelated to Dual spaceEquivalently0.60section
Super vector spacerelated to Linear transformationsThat0.60section
Super vector spacerelated to Linear transformationsAn0.60section
Super vector spacerelated to Linear transformationsThe0.60section
Super vector spacerelated to Linear transformationsHom0.60section
Super vector spacerelated to Operations on super vector spacesThe0.60section

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