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About: Complexification (Lie group)     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatLieAlgebrasyago:WikicatLieGroupsyago:Abstraction100002137yago:Algebra106012726yago:Cognition100023271yago:Content105809192yago:Discipline105996646yago:Group100031264yago:KnowledgeDomain105999266yago:Mathematics106000644yago:PsychologicalFeature100023100yago:PureMathematics106003682yago:Science105999797yago:WikicatAlgebraicGroups New Facet based on Instances of this Class

In mathematics, the complexification or universal complexification of a real Lie group is given by a continuous homomorphism of the group into a complex Lie group with the universal property that every continuous homomorphism of the original group into another complex Lie group extends compatibly to a complex analytic homomorphism between the complex Lie groups. The complexification, which always exists, is unique up to unique isomorphism. Its Lie algebra is a quotient of the complexification of the Lie algebra of the original group. They are isomorphic if the original group has a quotient by a discrete normal subgroup which is linear.