{"paper":{"title":"GK-dimension of the Lie algebra of generic $2\\times 2$ matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Gustavo Grings Machado, Plamen Koshlukov, Vesselin Drensky","submitted_at":"2015-03-06T21:25:03Z","abstract_excerpt":"Recently Machado and Koshlukov have computed the Gelfand-Kirillov dimension of the relatively free algebra $F_m=F_m(\\text{var}(sl_2(K)))$ of rank $m$ in the variety of algebras generated by the three-dimensional simple Lie algebra $sl_2(K)$ over an infinite field $K$ of characteristic different from 2. They have shown that $\\text{GKdim}(F_m)=3(m-1)$. The algebra $F_m$ is isomorphic to the Lie algebra generated by $m$ generic $2\\times 2$ matrices. Now we give a new proof for $\\text{GKdim}(F_m)$ using classical results of Procesi and Razmyslov combined with the observation that the commutator id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02091","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"}