Geodesic
Respectful Decompositions of Lie Algebras
Journal of Lie theory, Tome 34 (2024) no. 3, pp. 735-751
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One of Pierre Molino's principal mathematical achievements was his theory of Riemannian foliations. One of his last papers, published in 2001, showed that his theory could be extended to a large class of non-integrable distributions. The key example here is that of a \emph{respectful decomposition} of a Lie algebra $\mathfrak g$; this is vector space decomposition ${\mathfrak g} = H+V$ such that $[V,H]\subseteq H$. This paper will examine the basic properties of respectful decompositions.
Classification : 17B30, 58A30
Mots-clés : Nilpotent Lie algebra, geodesic 
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     author = {G. Cairns and Y. Nikolayevsky},
     title = {Respectful {Decompositions} of {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {735--751},
     year = {2024},
     volume = {34},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2024_34_3_JLT_2024_34_3_a12/}
}
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G. Cairns; Y. Nikolayevsky. Respectful Decompositions of Lie Algebras. Journal of Lie theory, Tome 34 (2024) no. 3, pp. 735-751. http://geodesic.mathdoc.fr/item/JLT_2024_34_3_JLT_2024_34_3_a12/