Inmathematics, theLie algebraE_7½ is a subalgebra ofE₈ containingE₇ defined by Landsberg and Manivel in orderto fill the "hole" in a dimension formula for theexceptional series E_n of simple Lie algebras. This hole was observed byCvitanovic,Deligne, Cohen and de Man. E_7½ has dimension 190, and is not simple: as a representation of its subalgebra E₇, it splits asE₇ ⊕ (56) ⊕R, where (56) is the 56-dimensionalirreducible representation of E₇. This representation has an invariantsymplectic form, and this symplectic form equips(56) ⊕R with the structure of aHeisenberg algebra; this Heisenberg algebra is thenilradical in E_7½.

• Vogel plane

• A.M. Cohen, R. de Man, "Computational evidence for Deligne's conjecture regarding exceptionalLie groups",Comptes rendus de l'Académie des Sciences, Série I 322 (1996) 427–432.
• P. Deligne, "La série exceptionnelle de groupes de Lie",Comptes rendus de l'Académie des Sciences, Série I 322 (1996) 321–326.
• P. Deligne, R. de Man, "La série exceptionnelle de groupes de Lie II",Comptes rendus de l'Académie des Sciences, Série I 323 (1996) 577–582.
• Landsberg, J. M.; Manivel, L. (2006), "The sextonions and E_7½",Advances in Mathematics,201 (1):143–179,arXiv:math.RT/0402157,doi:10.1016/j.aim.2005.02.001,MR 2204753

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