On the stochastic Lie algebra

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 $Aff(n-1,\mathbb{R})$. We prove that $\mathfrak{s}(n,\mathbb{R})$ is generated by two generic elements.

Cited by in corpus (3)

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