{"paper":{"title":"Semi-direct products involving $Sp_{2n}$ or $Spin_n$ with free algebras of symmetric invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitri I. Panyushev, Oksana S. Yakimova","submitted_at":"2018-02-20T14:39:20Z","abstract_excerpt":"This is a part of an ongoing project, the goal of which is to classify all semi-direct products $\\mathfrak s=\\mathfrak g{\\ltimes} V$ such that $\\mathfrak g$ is a simple Lie algebra, $V$ is a $\\mathfrak g$-module, and $\\mathfrak s$ has a free algebra of symmetric invariants. In this paper, we obtain such a classification for the representations of the orthogonal and symplectic algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07131","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"}