{"paper":{"title":"Some semi-direct products with free algebras of symmetric invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Oksana Yakimova","submitted_at":"2015-10-05T10:49:48Z","abstract_excerpt":"Let $\\mathfrak g$ be a complex reductive Lie algebra and $V$ the underling vector space of a finite-dimensional representation of $\\mathfrak g$. Then one can consider a new Lie algebra $\\mathfrak q=\\mathfrak g{\\ltimes} V$, which is a semi-direct product of $\\mathfrak g$ and an Abelian ideal $V$. We outline several results on the algebra $\\mathbb C[\\mathfrak q^*]^{\\mathfrak q}$ of symmetries invariants of $\\mathfrak q$ and describe all semi-direct products related to the defining representation of $\\mathfrak{sl}_n$ with $\\mathbb C[\\mathfrak q^*]^{\\mathfrak q}$ being a free algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01093","kind":"arxiv","version":3},"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"}