{"paper":{"title":"Invariant theory for non-reductive actions: extensions of Hilbert and Schwarz theorems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.AG","authors_text":"Leandro Nery","submitted_at":"2025-10-21T20:11:42Z","abstract_excerpt":"Classical invariant theory establishes a systematic correspondence between algebraic and smooth invariants for compact and reductive Lie groups. However, the extension of these results to non-compact and non-reductive regimes remains a subject of ongoing research. This paper examines the divergence between the algebras of polynomial and smooth invariants in two specific settings: discrete subgroups of the Lorentz group $O(n,1)$ acting on $\\mathbb{R}^{n,1}$, and cocompact actions on smooth manifolds. We prove that for discrete Lorentz groups, the ring of polynomial invariants is finitely genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.19053","kind":"arxiv","version":2},"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"}