Journal of Lie Theory

no. 3
Respectful Decompositions of Lie Algebras
Grant Cairns1; Yuri Nikolayevsky1
1Dept. of Mathematical and Physical Sciences, La Trobe University, Melbourne, Australia
Journal of Lie Theory, Volume 34 (2024) no. 3, pp. 735-751
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.
DOI: 10.5802/jolt.1358
Classification: 17B30, 58A30
Keywords: Nilpotent Lie algebra, geodesic

Grant Cairns  1 ; Yuri Nikolayevsky  1

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, Volume 34 (2024) no. 3, pp. 735-751. doi: 10.5802/jolt.1358
@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},
     doi = {10.5802/jolt.1358},
     zbl = {1567.17017},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1358/}
}
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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1358/
DO  - 10.5802/jolt.1358
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 https://jolt.centre-mersenne.org/articles/10.5802/jolt.1358/
%R 10.5802/jolt.1358
%F JOLT_2024_34_3_a12

Cited by Sources: