{"paper":{"title":"Lie subalgebras of differential operators on the super circle","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Shun-Jen Cheng, Weiqiang Wang","submitted_at":"2001-03-15T03:12:32Z","abstract_excerpt":"We classify anti-involutions of Lie superalgebra $\\hsd$ preserving the principal gradation, where $\\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations between the corresponding subalgebras fixed by these anti-involutions and subalgebras of $\\hat{gl}_{\\infty|\\infty}$ of types $OSP$ and $P$. We obtain a criterion for an irreducible highest weight module over these subalgebras to be quasifinite and construct free field realizations of a distinguished class of these modules. We further establish dualities between "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103092","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0103092/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}