# Assembling Lie Algebras from Lieons

@article{Vinogradov2012AssemblingLA, title={Assembling Lie Algebras from Lieons}, author={Alexandre M. Vinogradov}, journal={arXiv: Differential Geometry}, year={2012} }

If a Lie algebra structures $\gG$ on a vector space is the sum of a family of mutually compatible Lie algebra structures $\gG_i$, we say that $\gG$ is \emph{simply assembled} from $\gG_s$'s. By repeating this procedure several times one gets a family of Lie algebras \emph{assembled} from $\gG_s$'s. The central result of this paper is that any finite dimensional Lie algebra over $\R$ or $\C$ can be assembled from two constituents, called $\between$- and $\pitchfork$-\emph{lieons}. A lieon is the…

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