{"paper":{"title":"Automorphisms of the fine grading of sl(n,C) associated with the generalized Pauli matrices","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E. Pelantov\\'a, J. Patera, J. Tolar, M. Havl\\'i\\v{c}ek","submitted_at":"2003-11-10T15:50:54Z","abstract_excerpt":"We consider the grading of $sl(n,\\mathbb{C})$ by the group $\\Pi_n$ of generalized Pauli matrices. The grading decomposes the Lie algebra into $n^2-1$ one--dimensional subspaces. In the article we demonstrate that the normalizer of grading decomposition of $sl(n,\\mathbb{C})$ in $\\Pi_n$ is the group $SL(2, \\mathbb{Z}_n)$, where $\\mathbb{Z}_n$ is the cyclic group of order $n$. As an example we consider $sl(3,\\mathbb{C})$ graded by $\\Pi_3$ and all contractions preserving that grading. We show that the set of 48 quadratic equations for grading parameters splits into just two orbits of the normalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0311015","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"}