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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
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Landsberg, J. M.; Manivel, L. (2006), "A universal dimension formula for complex simple Lie algebras",
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of the Lie algebra (usually) decomposes as a sum of the complex numbers and 3 irreducible spaces
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on the symmetric square of the Lie algebra, which gives a point (α: β: γ) of
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128:(1996), "La série exceptionnelle de groupes de Lie",
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generalized Vogel's work to higher symmetric powers.
130:Comptes Rendus de l'Académie des Sciences, Série I
161:"On the exceptional series, and its descendants"
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64:, and is related by some observations made by
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60:of coordinates. It was introduced by
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70:Landsberg & Manivel (2006)
24:by eigenvalues α, β, γ of the
20:is a method of parameterizing
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180:10.1016/S1631-073X(02)02590-6
159:; Gross, Benedict H. (2002),
168:Comptes Rendus Mathématique
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255:The universal Lie algebra
229:10.1016/j.aim.2005.02.007
205:Advances in Mathematics
252:Vogel, Pierre (1999),
16:In mathematics, the
46:divided out by the
22:simple Lie algebras
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89:symmetric square
41:projective plane
26:Casimir operator
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174:(11): 877–881,
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48:symmetric group
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62:Vogel (1999)
58:permutations
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18:Vogel plane
273:Lie groups
267:Categories
258:, Preprint
119:References
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188:1631-073X
142:0764-4442
107:See also
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164:(PDF)
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101:C
97:B
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81:B
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54:3
51:S
44:P
37:3
34:S
32:/
30:P
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