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About: Vogel plane     Goto   Sponge   NotDistinct   Permalink

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Type: softwareyago:WikicatLieAlgebrasyago:WikicatLieGroupsyago:Abstraction100002137yago:Algebra106012726yago:Cognition100023271yago:Content105809192yago:Discipline105996646yago:Group100031264yago:KnowledgeDomain105999266yago:Mathematics106000644yago:PsychologicalFeature100023100yago:PureMathematics106003682yago:Science105999797 New Facet based on Instances of this Class

In mathematics, the Vogel plane is a method of parameterizing simple Lie algebras by eigenvalues α, β, γ of the Casimir operator on the symmetric square of the Lie algebra, which gives a point (α: β: γ) of P2/S3, the projective plane P2 divided out by the symmetric group S3 of permutations of coordinates. It was introduced by , and is related by some observations made by . generalized Vogel's work to higher symmetric powers.