About: Mutation (Jordan algebra)

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In mathematics, a mutation, also called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and only if the given element is invertible, in which case the mutation is called a proper mutation or an isotope. Mutations were first introduced by Max Koecher in his Jordan algebraic approach to Hermitian symmetric spaces and bounded symmetric domains of tube type. Their functorial properties allow an explicit construction of the corresponding Hermitian symmetric space of compact type as a compactification of a finite-dimensional complex semisimple Jordan algebra. The automorphism group of the compactification becomes a complex subgroup, the complexification of its maximal compact subgroup. Both groups act tra

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rdfs:label	Mutation (Jordan algebra) (en)
rdfs:comment	In mathematics, a mutation, also called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and only if the given element is invertible, in which case the mutation is called a proper mutation or an isotope. Mutations were first introduced by Max Koecher in his Jordan algebraic approach to Hermitian symmetric spaces and bounded symmetric domains of tube type. Their functorial properties allow an explicit construction of the corresponding Hermitian symmetric space of compact type as a compactification of a finite-dimensional complex semisimple Jordan algebra. The automorphism group of the compactification becomes a complex subgroup, the complexification of its maximal compact subgroup. Both groups act tra (en)
rdfs:seeAlso	Quadratic Jordan algebra Kantor–Koecher–Tits construction Structure group (Jordan algebra)
dcterms:subject	Complex manifolds Lie groups Non-associative algebras
Wikipage page ID	39366511 (xsd:integer)
Wikipage revision ID	1043758167 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadratic Jordan algebra Mutation (algebra) Euclidean Jordan algebra Complex manifolds Hua Luogeng Jordan algebra University of Virginia Jordan frame (Jordan algebra) Shilov boundary Quadratic representation Complexification (Lie group) Mathematics Möbius transformation Complex Lie group Complex manifold Complex projective space Symplectic group Maximal compact subgroup Algebraic variety American Mathematical Society Lie groups Upper half-plane Riemann sphere Atlas (topology) Albert algebra Non-associative algebras Killing form Biholomorphism Symmetric cone Hermitian symmetric space Max Koecher Zariski topology Siegel domain Jordan pair Jordan triple system Transition map Springer-Verlag Cartan criterion One-point compactification Lagrangian subspace Principal fiber bundle Smooth (algebraic variety) Bounded symmetric domain Structure group
Link from a Wikipage to an external page	https://books.google.com/books%3Fisbn=0387954473 http://www.math.virginia.edu/Faculty/McCrimmon/ http://www.math.uci.edu/~brusso/Meyberg(Reduced2).pdf http://molle.fernuni-hagen.de/~loos/jordan/archive/irvine/irvine.pdf%7Caccess-date=2013-05-12%7Carchive-url=https:/web.archive.org/web/20160303234008/http:/molle.fernuni-hagen.de/~loos/jordan/archive/irvine/irvine.pdf%7Carchive-date=2016-03-03%7Curl-status=dead http://projecteuclid.org/DPubS%3Fservice=UI&version=1.0&verb=Display&handle=euclid.nmj/1118785795%7Cdoi-access= http://www.mathunion.org/ICM/ICM1970.1/Main/icm1970.1.0279.0284.ocr.pdf http://www.math.tifr.res.in/~publ/ln/tifr45.pdf%7Cmr=0325715%7Clast=Jacobson%7Cfirst=
sameAs	Mutation (Jordan algebra) Mutation (Jordan algebra) Mutation (Jordan algebra) Mutation (Jordan algebra)
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has abstract	In mathematics, a mutation, also called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and only if the given element is invertible, in which case the mutation is called a proper mutation or an isotope. Mutations were first introduced by Max Koecher in his Jordan algebraic approach to Hermitian symmetric spaces and bounded symmetric domains of tube type. Their functorial properties allow an explicit construction of the corresponding Hermitian symmetric space of compact type as a compactification of a finite-dimensional complex semisimple Jordan algebra. The automorphism group of the compactification becomes a complex subgroup, the complexification of its maximal compact subgroup. Both groups act transitively on the compactification. The theory has been extended to cover all Hermitian symmetric spaces using the theory of Jordan pairs or Jordan triple systems. Koecher obtained the results in the more general case directly from the Jordan algebra case using the fact that only Jordan pairs associated with period two automorphisms of Jordan algebras are required. (en)
gold:hypernym	Algebra
prov:wasDerivedFrom	wikipedia-en:Mutation_(Jordan_algebra)?oldid=1043758167&ns=0
page length (characters) of wiki page	115068 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Mutation_(Jordan_algebra)
is rdfs:seeAlso of	Hermitian symmetric space
is Link from a Wikipage to another Wikipage of	Quadratic Jordan algebra Mutation (disambiguation) Isotope (Jordan algebra) Bergman operator Hermitian symmetric space

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