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In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups). It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams according to the table at right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B, despite the original construction not being symmetric, though gives a symmetric construction.

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rdf:type	Thing company yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264
rdfs:label	Freudenthal magic square (en) 프로이덴탈 마방진 (ko)
rdfs:comment	추상대수학에서 프로이덴탈 마방진(Freudenthal魔方陣, 영어: Freudenthal magic square)은 요르단 대수로부터 단순 리 대수를 구성하는 방법이다. 특히, 만약 요르단 대수를 실수 · 복소수 · 사원수 · 팔원수의 3×3 에르미트 행렬의 요르단 대수로 잡을 경우, 예외적 단순 리 대수 F₄ · G₂ · E₆ · E₇ · E₈을 대수적으로 구성할 수 있다. (ko) In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups). It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams according to the table at right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B, despite the original construction not being symmetric, though gives a symmetric construction. (en)
differentFrom	Magic square
dcterms:subject	Lie groups Representation theory
Wikipage page ID	13796065 (xsd:integer)
Wikipage revision ID	1118373932 (xsd:integer)
Link from a Wikipage to another Wikipage	Quaternion Euclidean Hurwitz algebra Euclidean Jordan algebra Trace-free Jordan algebra Dynkin diagram E7 (mathematics) Lie group Prehomogeneous vector space Complex number Mathematics Ruth Moufang Geometriae Dedicata Octonionic projective plane Mir Publishers Lagrangian Grassmannian Octonions Lie algebra Compact Lie algebra Composition algebra Derivation (abstract algebra) Journal of Algebra Mathematische Annalen Division algebra G2 (mathematics) Lie groups E6 (mathematics) E8 (mathematics) Ernest Vinberg Field (mathematics) Hans Freudenthal Riemannian symmetric space Hermitian matrix Jacques Tits Representation theory Advances in Mathematics Hermitian symmetric space Automorphism group Pierre Ramond Spin representation Split-complex number Split-octonions Split-quaternions Octonion Real number Triality F4 (mathematics) Exceptional Lie group List of simple Lie groups Jordan triple system Normed division algebra John Frank Adams Cayley projective plane Classical Lie group dbr:Double_Lagrangian_Grassmannian dbr:Tony_Sudbery
Link from a Wikipage to an external page	https://www.ams.org/journals/bull/2005-42-02/S0273-0979-05-01052-9/S0273-0979-05-01052-9.pdf http://math.ucr.edu/home/baez/octonions/ https://archive.org/details/einsteinmanifold0000bess http://www.ims.cuhk.edu.hk/~leung/PhD%20students/Thesis%20Yong%20Dong%20Huang.pdf http://math.ucr.edu/home/baez/octonions/node16.html http://inspirehep.net/record/111550
sameAs	Freudenthal magic square Freudenthal magic square Freudenthal magic square Freudenthal magic square Freudenthal magic square Freudenthal magic square
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has abstract	In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups). It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently. It associates a Lie algebra to a pair of division algebras A, B. The resulting Lie algebras have Dynkin diagrams according to the table at right. The "magic" of the Freudenthal magic square is that the constructed Lie algebra is symmetric in A and B, despite the original construction not being symmetric, though gives a symmetric construction. The Freudenthal magic square includes all of the exceptional Lie groups apart from G2, and it provides one possible approach to justify the assertion that "the exceptional Lie groups all exist because of the octonions": G2 itself is the automorphism group of the octonions (also, it is in many ways like a classical Lie group because it is the stabilizer of a generic 3-form on a 7-dimensional vector space – see prehomogeneous vector space). (en) 추상대수학에서 프로이덴탈 마방진(Freudenthal魔方陣, 영어: Freudenthal magic square)은 요르단 대수로부터 단순 리 대수를 구성하는 방법이다. 특히, 만약 요르단 대수를 실수 · 복소수 · 사원수 · 팔원수의 3×3 에르미트 행렬의 요르단 대수로 잡을 경우, 예외적 단순 리 대수 F₄ · G₂ · E₆ · E₇ · E₈을 대수적으로 구성할 수 있다. (ko)
gold:hypernym	Construction

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