{"paper":{"title":"Complexity of simple modules over the Lie superalgebra $\\mathfrak{osp}(k|2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Houssein El Turkey","submitted_at":"2016-02-03T16:45:05Z","abstract_excerpt":"The complexity of a module is the rate of growth of the minimal projective resolution of the module while the $z$-complexity is the rate of growth of the number of indecomposable summands at each step in the resolution. Let $\\mathfrak{g}=\\mathfrak{osp}(k|2)$ ($k>2$) be the type II orthosymplectic Lie superalgebra of types $B$ or $D$. In this paper, we compute the complexity and the $z$-complexity of the simple finite-dimensional $\\mathfrak{g}$-supermodules. We then give geometric interpretations using support and associated varieties for these complexities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01361","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"}