
Journal of Lie Theory 34 (2024), No. 3, 735751 Copyright Heldermann Verlag 2024 Respectful Decompositions of Lie Algebras Grant Cairns Dept. of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia G.Cairns@latrobe.edu.au Yuri Nikolayevsky Dept. of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia Y.Nikolayevsky@latrobe.edu.au [Abstractpdf] 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 nonintegrable 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. Keywords: Nilpotent Lie algebra, geodesic. MSC: 17B30, 58A30. [ Fulltextpdf (153 KB)] for subscribers only. 