On the stochastic Lie algebra

2018/05/18 by Manuel Guerra, Guerra, Manuel, Andrey Sarychev +1 · 1 citation
Mathematics · #17B45 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1805.07299

openalex publication_date 2018/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the structure of the Lie algebra \mathfraks(n,\mathbb R) corresponding to the so-called stochastic Lie group S (n,\mathbb R). We obtain the Levi decomposition of the Lie algebra, classify Levi factor and classify the representation of the factor in ℝⁿ. We discuss isomorphism of 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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