Journal of Lie Theory 34 (2024), No. 3, 735--751
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
[Abstract-pdf]
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.
Keywords: Nilpotent Lie algebra, geodesic.
MSC: 17B30, 58A30.
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