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arXiv · 2207.03068

Respectful decompositions of Lie algebras

Grant Cairns·Yuri Nikolayevsky
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Abstract

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.

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Grant Cairns, Yuri Nikolayevsky. 2022-07-07. Respectful decompositions of Lie algebras. https://arxiv.org/abs/2207.03068

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