Let U be a real vector space, B an inner product on U and a 3-form. The 3-form T defines two natural maps, and given by and . We show that is a Lie bracket if and only if is a Lie subalgebra of .
Soit U un espace vectoriel réel, B un produit euclidien sur U et une 3-forme. La 3-forme T permet de définir deux applications, et telles que et . On va démontrer que est un crochet de Lie si et seulement si est une sous-algèbre de Lie de .
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@article{CRMATH_2006__342_6_381_0, author = {Rohr, Rudolf Philippe}, title = {Lie algebras generated by 3-forms}, journal = {Comptes Rendus. Math\'ematique}, pages = {381--385}, publisher = {Elsevier}, volume = {342}, number = {6}, year = {2006}, doi = {10.1016/j.crma.2006.01.006}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2006.01.006/} }
TY - JOUR AU - Rohr, Rudolf Philippe TI - Lie algebras generated by 3-forms JO - Comptes Rendus. Mathématique PY - 2006 SP - 381 EP - 385 VL - 342 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.01.006/ DO - 10.1016/j.crma.2006.01.006 LA - en ID - CRMATH_2006__342_6_381_0 ER -
Rohr, Rudolf Philippe. Lie algebras generated by 3-forms. Comptes Rendus. Mathématique, Volume 342 (2006) no. 6, pp. 381-385. doi : 10.1016/j.crma.2006.01.006. http://www.numdam.org/articles/10.1016/j.crma.2006.01.006/
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