E7

In mathematics, the Lie algebra E 7½ is a subalgebra of E 8 containing E 7 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 E 7 , it splits as , where (56) is the 56-dimensional irreducible representation of E 7 . 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 E 7½ .

E7, E07, E-7 or E 7 may refer to: ==Science and engineering== E7 liquid crystal mixture E 7 (mathematics), an exceptional Lie group, or its Lie algebra \mathfrak e_7 E 7 polytope, in geometry E7 papillomavirus protein E7 European long distance path ==Transport== EMD E7, a diesel locomotive European route E07, an international road Peugeot E7, a hackney cab PRR E7, a steam locomotive Carbon Motors E7, a police car E7 series, a Japanese high-speed train Nihonkai-Tōhoku Expressway and Akita Expressway (between Kawabe JCT and Kosaka JCT), route E7 in Japan Cheras–Kajang Expressway, route E7 in Malaysia Foton Smart Smurf E7, a Chinese battery electric van ==Other uses== Boeing E-7, either: Boeing E-7 ARIA, the original designation assigned by the United States Air Force under the Mission Designation System to the EC-18B Advanced Range Instrumentation Aircraft. Boeing E-7 Wedgetail, the designation assigned by the Royal Australian Air Force to the Boeing 737 AEW&C (airborne early warning and control) aircraft. Economy 7, an electricity tariff E-7 enlisted rank in the military of the United States E7, a musical note in the seventh octave E-7, the original designation for the EC-18 ARIA electronic warfare aircraft E7, a postcode district in the E postcode area for east London European Aviation Air Charter, by IATA airline designator Nokia E7, a smart phone Samsung Galaxy E7, a smart phone E07, a number station allegedly used by Russia, and nicknamed "The English Man" Eureka Seven ==See also== 7E (disambiguation)

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