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Vogel plane : ウィキペディア英語版
Vogel plane
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 ''P''2/''S''3, the projective plane ''P''2 divided out by the symmetric group ''S''3 of permutations of coordinates. It was introduced by , and is related by some observations made by . generalized Vogel's work to higher symmetric powers.
The point of the projective plane (modulo permutations) corresponding to a simple complex Lie algebra is given by three eigenvalues α, β, γ of the Casimir operator acting on spaces ''A'', ''B'', ''C'', where the symmetric square of the Lie algebra (usually) decomposes as a sum of the complex numbers and 3 irreducible spaces ''A'', ''B'', ''C''.
==See also==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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