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.
1
Dept. of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia
Grant Cairns; Yuri Nikolayevsky. Respectful Decompositions of Lie Algebras. Journal of Lie Theory, Tome 34 (2024) no. 3, pp. 735-751. http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a12/
@article{JOLT_2024_34_3_a12,
author = {Grant Cairns and Yuri 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/JOLT_2024_34_3_a12/}
}
TY - JOUR
AU - Grant Cairns
AU - Yuri Nikolayevsky
TI - Respectful Decompositions of Lie Algebras
JO - Journal of Lie Theory
PY - 2024
SP - 735
EP - 751
VL - 34
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a12/
ID - JOLT_2024_34_3_a12
ER -
%0 Journal Article
%A Grant Cairns
%A Yuri Nikolayevsky
%T Respectful Decompositions of Lie Algebras
%J Journal of Lie Theory
%D 2024
%P 735-751
%V 34
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a12/
%F JOLT_2024_34_3_a12
