E7½
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In mathematics, the Lie algebra E7½ is a subalgebra of E8 containing E7 defined by Landsberg and  Manivel in order
to fill the "hole" in a dimension formula for the exceptional series En of simple Lie algebras. This hole was observed by Cvitanovic, Deligne, Cohen and de Man. E7½ has dimension 190, and is not simple: as a representation of its subalgebra E7, it splits as , where (56) is the 56-dimensional irreducible representation of E7. This representation has an invariant symplectic form, and this symplectic form equips  with the structure of a Heisenberg algebra; this Heisenberg algebra is the nilradical in E7½.

See also

Vogel plane

References
 A.M. Cohen, R. de Man, "Computational evidence for Deligne's conjecture regarding exceptional Lie 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.

Lie groups