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- Vogel_plane abstract "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 Vogel (1999), and is related by some observations made by Deligne (1996). Landsberg & Manivel (2006) 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.".
- Vogel_plane wikiPageID "31677432".
- Vogel_plane wikiPageLength "2105".
- Vogel_plane wikiPageOutDegree "9".
- Vogel_plane wikiPageRevisionID "596867109".
- Vogel_plane wikiPageWikiLink Casimir_element.
- Vogel_plane wikiPageWikiLink Category:Lie_algebras.
- Vogel_plane wikiPageWikiLink Category:Lie_groups.
- Vogel_plane wikiPageWikiLink E7½.
- Vogel_plane wikiPageWikiLink Permutation.
- Vogel_plane wikiPageWikiLink Projective_plane.
- Vogel_plane wikiPageWikiLink Simple_Lie_group.
- Vogel_plane wikiPageWikiLink Symmetric_algebra.
- Vogel_plane wikiPageWikiLink Symmetric_group.
- Vogel_plane wikiPageWikiLinkText "Vogel plane".
- Vogel_plane wikiPageUsesTemplate Template:Citation.
- Vogel_plane wikiPageUsesTemplate Template:Harvtxt.
- Vogel_plane subject Category:Lie_algebras.
- Vogel_plane subject Category:Lie_groups.
- Vogel_plane hypernym Method.
- Vogel_plane type Software.
- Vogel_plane type Algebra.
- Vogel_plane comment "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 Vogel (1999), and is related by some observations made by Deligne (1996). Landsberg & Manivel (2006) generalized Vogel's work to higher symmetric powers.".
- Vogel_plane label "Vogel plane".
- Vogel_plane sameAs Q7939378.
- Vogel_plane sameAs m.0gmbxqw.
- Vogel_plane sameAs Q7939378.
- Vogel_plane wasDerivedFrom Vogel_plane?oldid=596867109.
- Vogel_plane isPrimaryTopicOf Vogel_plane.