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Complex Lie group

In geometry, a complex Lie group is a Lie group over the complex numbers; i.e., it is a complex-analytic manifold that is also a group in such a way G × G → G , ( x , y ) ↦ x y − 1 {\displaystyle G\times G\to G,(x,y)\mapsto xy^{-1}} is holomorphic. Basic examples are GL n ⁡ ( C ) {\displaystyle \operatorname {GL} _{n}(\mathbb {C} )} , the general linear…

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Complex Lie group

Nodes20
Edges19
Triples28
Avg. degree1.9
Density0.1
Components1

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Complex Lie group

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related to Examples · 13
Complex Lie group → Aut, For, Gamma, GL, If, Indeed, It, Kähler, Let, Lie, Since, Then, TX
related to References · 13
Complex Lie group → Boca Raton, Chapman, Complex Lie Groups, Dong Hoon, Florida, Gèbres, Hall/CRC, ISBN, Jean-Pierre, L'Enseignement Mathématique, Lee, MR, The Structure
is a · 2
Complex Lie group → complex Lie algebra, Lie group over the complex numbers

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Important terminology

complex group lie displaystyle mathbb operatorname algebraic linear compact gl manifold groups connected algebra numbers semisimple holomorphic structure examples vector

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Complex Lie groupis aLie group over the complex numbers0.90text
Complex Lie groupis acomplex Lie algebra0.90text
Complex Lie grouprelated to ExamplesLie0.60section
Complex Lie grouprelated to ExamplesIndeed0.60section
Complex Lie grouprelated to ExamplesSince0.60section
Complex Lie grouprelated to ExamplesGL0.60section
Complex Lie grouprelated to ExamplesLet0.60section
Complex Lie grouprelated to ExamplesThen0.60section
Complex Lie grouprelated to ExamplesAut0.60section
Complex Lie grouprelated to ExamplesGamma0.60section
Complex Lie grouprelated to ExamplesTX0.60section
Complex Lie grouprelated to ExamplesIt0.60section

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