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Scientific article
English

Lie algebras generated by 3-forms

Publication date2006
Abstract

Let U be a real vector space, B an inner product on U and T ∈ ∧U ∗ a 3-form. The 3-form T defines two natural maps, [·,·] U :∧2U →U and σ :U →∧2U ∗ ∼= so(U,B) given by [x,y] U = 2B#(T (x, y, ·)) and σ(x) = T (x, ·, ·). We show that [·,·] U is a Lie bracket if and only if gT ≡ Im(σ ) is a Lie subalgebra of so(U,B).

Citation (ISO format)
ROHR, Rudolf Philippe. Lie algebras generated by 3-forms. In: Comptes rendus de l’Académie des sciences. Série 1, Mathématique, 2006, vol. 342, n° 6, p. 381–385. doi: 10.1016/j.crma.2006.01.006
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ISSN of the journal0764-4442
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