{"paper":{"title":"Universal central extensions of $\\mathfrak{sl}(m, n, A)$ of small rank over associative superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Manuel Ladra, Xabier Garc\\'ia-Mart\\'inez","submitted_at":"2014-05-15T23:30:41Z","abstract_excerpt":"We complete the solution of the problem of finding the universal central extension of the matrix superalgebras $\\mathfrak{sl}(m, n, A)$ where $A$ is an associative superalgebra and computing $H_2\\big(\\mathfrak{sl}(m, n, A)\\big)$. The Steinberg Lie superalgebra $\\mathfrak{st}(m, n, A)$ has a very important role and we will also find out $H_2\\big(\\mathfrak{st}(m, n, A)\\big)$. In Chen and Sun (arXiv:1311.7079, 2013) it is solved the problem where $m+n \\geq 5$ and in Chen and Guay (Algebr. Represent. Theory, 2013) it is solved when $n=0$, so here we work out the three remaining cases $\\mathfrak{sl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4035","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"}