In mathematics, the Lie algebra E_7½ 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 E_n of simple Lie algebras. This hole was observed by Cvitanovic, Deligne, Cohen and de Man. E_7½ has dimension 190, and is not simple: as a representation of its subalgebra E₇, it splits as E₇ ⊕ (56) ⊕ R, where (56) is the 56-dimensional irreducible representation of E₇. This representation has an invariant symplectic form, and this symplectic form equips (56) ⊕ R with the structure of a Heisenberg algebra; this Heisenberg algebra is the nilradical in E_7½.

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.

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E7 (countries)

The E7 is a group of seven countries with emerging economies. The E7 are predicted to have larger economies than the G7 countries by 2020. The term was coined by the PricewaterhouseCoopers in the Stern Review report, which was published on 30 October 2006. The E7 represents the seven major emerging economies.

Below are the E7 countries and their predicted economies in 2050 as predicted by Goldman Sachs:

The "Emerging 7" according to Peter Marber (author of Seeing the Elephant (2009)) states the 7 countries as follows: China, Russia, India, Indonesia, Mexico, Brazil and South Korea—as opposed to Turkey. The back-study to this is South Korea's rapid economic growth in 3 decades paired with enrollment rates (between 1966 to 1995); compared to the growth of the UK (150 years) and the US (100 years).