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Lie algebras generated by 3-forms

Published in Comptes Rendus de l'Académie des Sciences. I, Mathematics. 2006, vol. 342, no. 6, p. 381 - 385
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).
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ROHR, Rudolf Philippe. Lie algebras generated by 3-forms. In: Comptes Rendus de l'Académie des Sciences. I, Mathematics, 2006, vol. 342, n° 6, p. 381 - 385. https://archive-ouverte.unige.ch/unige:12091

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Deposited on : 2010-10-14

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