{"paper":{"title":"Endotrivial modules for the general linear Lie superalgebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrew J. Talian","submitted_at":"2015-04-15T22:04:43Z","abstract_excerpt":"If $\\mathfrak{g} = \\mathfrak{g}_{\\overline{0}} \\oplus \\mathfrak{g}_{\\overline{1}}$ is a Lie superalgebra over an algebraically closed field $k$ of characteristic 0, the notion of an endotrivial module has recently been extended to $\\mathfrak{g}$-modules by defining $M$ to be endotrivial if $\\operatorname{Hom}_k(M,M) \\cong k_{ev} \\oplus P$ as $\\mathfrak{g}$-supermodules. Here, $k_{ev}$ denotes the trivial module concentrated in degree $\\overline{0}$ and $P$ is a $(U(\\mathfrak{g}), U(\\mathfrak{g}_{\\overline{0}}))$-projective supermodule. In the stable module category, these modules form a group "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04059","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"}