{"paper":{"title":"Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Brian D. Boe, Daniel K. Nakano, Jonathan R. Kujawa","submitted_at":"2011-07-13T15:30:35Z","abstract_excerpt":"Let $\\mathfrak{g}=\\mathfrak{g}_{\\bar{0}}\\oplus \\mathfrak{g}_{\\bar{1}}$ be a classical Lie superalgebra and $\\mathcal{F}$ be the category of finite dimensional $\\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\\mathfrak{g}_{\\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\\mathfrak{g}_{\\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2579","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"}