Lie algebras generated by 3-forms

Rohr, Rudolf Philippe

doi:10.1016/j.crma.2006.01.006

Scientific article

English

Lie algebras generated by 3-forms

ContributorsRohr, Rudolf Philippe

Published inComptes rendus de l'Académie des sciences. Série 1, Mathématique, vol. 342, no. 6, p. 381-385

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).

Affiliation entities

Faculté des sciences / Section de mathématiques

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

Article (Published version)

Identifiers

PID : unige:12091
DOI : 10.1016/j.crma.2006.01.006

Additional URL for this publicationhttp://linkinghub.elsevier.com/retrieve/pii/S1631073X0600015X

Journal ISSN0764-4442

549views

0downloads

Creation12/10/2010 13:53:00

First validation12/10/2010 13:53:00

Update time14/03/2023 16:07:28

Status update14/03/2023 16:07:28

Last indexation29/10/2024 17:14:49

Archive ouverte UNIGE

Lie algebras generated by 3-forms

Technical informations