{"paper":{"title":"Lifting automorphisms of quotients of adjoint representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Gerald W. Schwarz","submitted_at":"2013-01-26T23:53:41Z","abstract_excerpt":"Let $\\mathfrak g_i$ be a simple complex Lie algebra, $1\\leq i \\leq d$, and let $G=G_1\\times...\\times G_d$ be the corresponding adjoint group. Consider the $G$-module $V=\\oplus r_i\\mathfrak g_i$ where $r_i\\geq 1$ for all $i$. We say that $V$ is \\emph{large} if all $r_i\\geq 2$ and $r_i\\geq 3$ if $G_i$ has rank 1. In [Schwarz12] we showed that when $V$ is large any algebraic automorphism $\\psi$ of the quotient $Z:= V//G$ lifts to an algebraic mapping $\\Psi\\colon V\\to V$ which sends the fiber over $z$ to the fiber over $\\psi(z)$, $z\\in Z$. (Most cases were already handled in [Kuttler11]). We also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6300","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"}