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An endotrivial $\\mathfrak{g}$-module, $M$, is a $\\mathfrak{g}$-supermodule such that $\\operatorname{Hom}_k(M,M) \\cong k_{ev} \\oplus P$ as $\\mathfrak{g}$-supermodules, where $k_{ev}$ is the trivial module concentrated in degree $\\overline{0}$ and $P$ is a projective $\\mathfrak{g}$-supermodule. In the stable module category, these modules form a group under the operation of the tensor product. We show that for an endotrivial modul"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1306.2582","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-11T17:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"a75d8b7f67796e8bfe2209074c4f49110330fd84a1c93ef04b49ae8ecde3bcb7","abstract_canon_sha256":"7fb32f1a976a8a0f919e70d390742ac04a8cb77a95e91cb2c59d3d498b568481"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:41.154380Z","signature_b64":"hCbOzs9cR0nOn6wa4Nf/+jWnUaukbU+cqMIfwD8yGa+OsX68f3n8sRB0Qipmi496U+OmXnzdeClo+HcII0SDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"224f9f237ce420c0f0275c68dc0cb6283d41a88e51e7df5e88b0b2fb120b0101","last_reissued_at":"2026-05-18T02:18:41.153717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:41.153717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On endotrivial modules for Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Andrew J. Talian","submitted_at":"2013-06-11T17:02:34Z","abstract_excerpt":"Let $\\mathfrak{g} = \\mathfrak{g}_{\\overline{0}} \\oplus \\mathfrak{g}_{\\overline{1}}$ be a Lie superalgebra over an algebraically closed field, $k$, of characteristic 0. An endotrivial $\\mathfrak{g}$-module, $M$, is a $\\mathfrak{g}$-supermodule such that $\\operatorname{Hom}_k(M,M) \\cong k_{ev} \\oplus P$ as $\\mathfrak{g}$-supermodules, where $k_{ev}$ is the trivial module concentrated in degree $\\overline{0}$ and $P$ is a projective $\\mathfrak{g}$-supermodule. In the stable module category, these modules form a group under the operation of the tensor product. We show that for an endotrivial modul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2582","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1306.2582","created_at":"2026-05-18T02:18:41.153815+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.2582v3","created_at":"2026-05-18T02:18:41.153815+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2582","created_at":"2026-05-18T02:18:41.153815+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJHZ6I344QQM","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJHZ6I344QQMB4BH","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJHZ6I34","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA","json":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA.json","graph_json":"https://pith.science/api/pith-number/EJHZ6I344QQMB4BHLRUNYDFWFA/graph.json","events_json":"https://pith.science/api/pith-number/EJHZ6I344QQMB4BHLRUNYDFWFA/events.json","paper":"https://pith.science/paper/EJHZ6I34"},"agent_actions":{"view_html":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA","download_json":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA.json","view_paper":"https://pith.science/paper/EJHZ6I34","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.2582&json=true","fetch_graph":"https://pith.science/api/pith-number/EJHZ6I344QQMB4BHLRUNYDFWFA/graph.json","fetch_events":"https://pith.science/api/pith-number/EJHZ6I344QQMB4BHLRUNYDFWFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA/action/storage_attestation","attest_author":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA/action/author_attestation","sign_citation":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA/action/citation_signature","submit_replication":"https://pith.science/pith/EJHZ6I344QQMB4BHLRUNYDFWFA/action/replication_record"}},"created_at":"2026-05-18T02:18:41.153815+00:00","updated_at":"2026-05-18T02:18:41.153815+00:00"}