{"paper":{"title":"On the stochastic Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Andrey Sarychev, Manuel Guerra","submitted_at":"2018-05-18T15:40:10Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07299","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}