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In mathematics, essential dimension is an invariant defined for certain algebraic structures such as algebraic groups and quadratic forms. It was introduced by J. Buhler and Z. Reichsteinand in its most generality defined by A. Merkurjev.

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rdfs:label	Essential dimension (en)
rdfs:comment	In mathematics, essential dimension is an invariant defined for certain algebraic structures such as algebraic groups and quadratic forms. It was introduced by J. Buhler and Z. Reichsteinand in its most generality defined by A. Merkurjev. (en)
dct:subject	Algebraic structures
Wikipage page ID	16950168 (xsd:integer)
Wikipage revision ID	1068301971 (xsd:integer)
Link from a Wikipage to another Wikipage	Root of unity Basis (linear algebra) Algebraic group Algebraic structure Algebraic torus Algebraically closed field Homomorphism Vector space Invariant (mathematics) Galois field Mathematics Morphism Functor Spin group Algebraic structures Category of sets Torsor Joe P. Buhler Lattice (group) Linear algebraic group Alexander Merkurjev Field (mathematics) Faithful representation Isomorphism class Quadratic form Representation (mathematics) Prime number Characteristic (algebra) Supremum Cokernel Zinovy Reichstein Moduli of algebraic curves Field extension Coprime Natural number Category (mathematics) Symmetric group Flat topology P-group Transcendence degree Fibered category Intermediate field
sameAs	Essential dimension Essential dimension Essential dimension Essential dimension
dbp:wikiPageUsesTemplate	dbt:Math dbt:Reflist dbt:OEIS2C
has abstract	In mathematics, essential dimension is an invariant defined for certain algebraic structures such as algebraic groups and quadratic forms. It was introduced by J. Buhler and Z. Reichsteinand in its most generality defined by A. Merkurjev. Basically, essential dimension measures the complexity of algebraic structures via their fields of definition. For example, a quadratic form q : V → K over a field K, where V is a K-vector space, is said to be defined over a subfield L of K if there exists a K-basis e1,...,en of V such that q can be expressed in the form with all coefficients aij belonging to L. If K has characteristic different from 2, every quadratic form is diagonalizable. Therefore, q has a field of definition generated by n elements. Technically, one always works over a (fixed) base field k and the fields K and L in consideration are supposed to contain k. The essential dimension of q is then defined as the least transcendence degree over k of a subfield L of K over which q is defined. (en)
prov:wasDerivedFrom	wikipedia-en:Essential_dimension?oldid=1068301971&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Essential_dimension
is Link from a Wikipage to another Wikipage of	House system at the California Institute of Technology Spin group Essential Dimension Joe P. Buhler Linear algebraic group Alexander Merkurjev Cole Prize Zinovy Reichstein Reductive group
is Wikipage redirect of	Essential Dimension
is known for of	Zinovy Reichstein
is known for of	Alexander Merkurjev Zinovy Reichstein
is foaf:primaryTopic of	wikipedia-en:Essential_dimension

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