E7½ (Lie algebra)
Encyclopedia : E : E7 : E7L : E7½ (Lie algebra)
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 the exceptional series of Lie algebras observed by Cvitanovic, Deligne, Cohen and de Man. It has dimension 190, and as a representation of its subalgebra E7 splits as E7 ⊕ (56) ⊕ R, where (56) is the 56 dimensional irreducible representation of E7.
References
- A.M. Cohen, R. de Man, Computational evidence for Deligne's conjecture regarding exceptional Lie groups, C. R. Acad. Sci. Paris, Série I 322 (1996) 427--432.
- P. Deligne, La série exceptionnelle de groupes de Lie, C. R. Acad. Sci. Paris, Série I 322 (1996) 321--326.
- P. Deligne, R. de Man, La série exceptionnelle de groupes de Lie II, C. R. Acad. Sci. Paris, Série I 323 (1996) 577--582.
- Landsberg, J. M. Manivel, L. [The sextonions and E7½]. Adv. Math. 201 (2006), no. 1, 143--179.
| Exceptional Lie groups |
| E6 | E7 | E7½ | E8 | F4 | G2 |
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