e/E₆

Information
has gloss	eng: In mathematics, E6 is the name of some Lie groups and also their Lie algebras \mathfrake}_6. It is one of the five exceptional compact simple Lie groups as well as one of the simply laced groups. E6 has rank 6 and dimension 78. The fundamental group of the compact form is the cyclic group Z3 and its outer automorphism group is the cyclic group Z2. Its fundamental representation is 27-dimensional (complex), and a basis is given by the 27 lines on a cubic surface. The dual representation, which is inequivalent, is also 27-dimensional.
lexicalization	eng: E6
lexicalization	eng: E<sub>6</sub> (mathematics)
lexicalization	eng: E₆
instance of	e/Lie group

Meaning
French
has gloss	fra: En mathématiques, E6 est le nom dun groupe de Lie ; son algèbre de Lie est notée \mathfrake}_6. Il sagit de lun des cinq groupes de Lie complexes de type exceptionnel. E6 est de rang 6 et de dimension 78. Le groupe fondamental de sa forme compacte est le groupe cyclique Z3 et son groupe dautomorphismes est le groupe cyclique Z2. Sa représentation fondamentale est de dimension complexe 27. Sa représentation duale est également de dimension 27.
lexicalization	fra: E6
Italian
has gloss	ita: In matematica, E6 è la sigla che contraddistingue un gruppo di Lie e la sua algebra di Lie \mathfrake}_6. Il gruppo E6 è uno dei cinque gruppi di Lie semplici eccezionali e uno dei gruppi semplicemente allacciati.
lexicalization	ita: E6
Russian
has gloss	rus: E6 — название некоторых групп Ли и также их алгебр Ли \mathfrake}_6. E6 — одна из пяти компактных простых групп Ли. E6 имеет ранг 6 и размерность 78.
lexicalization	rus: E6