On the stochastic Lie algebra

Manuel Guerra; Andrey Sarychev

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arXiv · 1805.07299

On the stochastic Lie algebra

Manuel Guerra·Andrey Sarychev

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Abstract

We study the structure of the Lie algebra $\mathfrak{s}(n,\mathbb R)$ corresponding to the so-called stochastic Lie group $\mathcal{S} (n,\mathbb R)$. We obtain the Levi decomposition of the Lie algebra, classify Levi factor and classify the representation of the factor in $\mathbb{R}^n$. We discuss isomorphism of $\mathcal{S}(n,\mathbb R)$ with the group of invertible affine maps ${\it Aff}(n-1,\mathbb R)$. We prove that $\mathfrak s(n, \mathbb R)$ is generated by two generic elements.

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Manuel Guerra, Andrey Sarychev. 2018-05-18. On the stochastic Lie algebra. https://arxiv.org/abs/1805.07299

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