About: Universal geometric algebra

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In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form. Some authors restrict this to the infinite-dimensional case. When n = ∞, i.e. there are countably many dimensions, then is called simply the universal geometric algebra (UGA), which contains vector spaces such as Rp, q and their respective geometric algebras . UGA contains all finite-dimensional geometric algebras (GA). One may generate a finite-dimensional GA by choosing a unit pseudoscalar (I). The set of all vectors that satisfy

Attributes	Values
rdfs:label	Universal geometric algebra (en)
rdfs:comment	In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form. Some authors restrict this to the infinite-dimensional case. When n = ∞, i.e. there are countably many dimensions, then is called simply the universal geometric algebra (UGA), which contains vector spaces such as Rp, q and their respective geometric algebras . UGA contains all finite-dimensional geometric algebras (GA). One may generate a finite-dimensional GA by choosing a unit pseudoscalar (I). The set of all vectors that satisfy (en)
dcterms:subject	Geometric algebra
Wikipage page ID	39229208 (xsd:integer)
Wikipage revision ID	1096997735 (xsd:integer)
Link from a Wikipage to another Wikipage	Power of two Pseudo-Euclidean space Scalar (mathematics) Geometric algebra Vector space Conformal geometric algebra Mathematics Geometric calculus Orientation (vector space) Clifford algebra Geometric algebra Tangent space Affine connection Fiber bundle Dimension (vector space) Quadratic form Bivector Differential geometry Manifold Infinite-dimensional Metric tensor Real coordinate space Real number Pseudoscalar Up to Countably many Abelian algebra
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=O7jO2pmUFOgC&pg=PA371 https://books.google.com/books%3Fid=VW4yt0WHdjoC%7Cdate=2003-05-29 https://books.google.com/books%3Fid=bUEcbyfW55YC%7Cyear=2008 https://books.google.com/books%3Fid=dScR5zwrheYC%7Cdate=1987-08-31
sameAs	Universal geometric algebra Universal geometric algebra Universal geometric algebra
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:How dbt:Math dbt:Mvar dbt:Reflist
has abstract	In mathematics, a universal geometric algebra is a type of geometric algebra generated by real vector spaces endowed with an indefinite quadratic form. Some authors restrict this to the infinite-dimensional case. The universal geometric algebra of order 22n is defined as the Clifford algebra of 2n-dimensional pseudo-Euclidean space Rn, n. This algebra is also called the "mother algebra". It has a nondegenerate signature. The vectors in this space generate the algebra through the geometric product. This product makes the manipulation of vectors more similar to the familiar algebraic rules, although non-commutative. When n = ∞, i.e. there are countably many dimensions, then is called simply the universal geometric algebra (UGA), which contains vector spaces such as Rp, q and their respective geometric algebras . UGA contains all finite-dimensional geometric algebras (GA). The elements of UGA are called multivectors. Every multivector can be written as the sum of several r-vectors. Some r-vectors are scalars (r = 0), vectors (r = 1) and bivectors (r = 2). One may generate a finite-dimensional GA by choosing a unit pseudoscalar (I). The set of all vectors that satisfy is a vector space. The geometric product of the vectors in this vector space then defines the GA, of which I is a member. Since every finite-dimensional GA has a unique I (up to a sign), one can define or characterize the GA by it. A pseudoscalar can be interpreted as an n-plane segment of unit area in an n-dimensional vector space. (en)
prov:wasDerivedFrom	wikipedia-en:Universal_geometric_algebra?oldid=1096997735&ns=0
page length (characters) of wiki page	8287 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Universal_geometric_algebra
is Link from a Wikipage to another Wikipage of	Mother algebra Geometric algebra UGA Vector Manifold Vector manifold
is Wikipage redirect of	Mother algebra Vector Manifold Vector manifold
is Wikipage disambiguates of	UGA
is foaf:primaryTopic of	wikipedia-en:Universal_geometric_algebra

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