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We construct two infinite dimensional intermediate series modules of 3-Lie algebra $A_{\\omega}^{\\delta}$, and two infinite dimensional modules $(V, \\psi_{\\lambda\\mu})$ and $(V, \\phi_{\\mu})$ of the Lie algebra\n  ad$(A_{\\omega}^{\\delta})$, and prove that only $(V, \\psi_{\\lambda0})$ and $(V, \\psi_{\\lambda1})$ are induced modules."},"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":"1904.11196","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-25T08:14:00Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8efa586cd80a30e322cd9d9922db99fe8a35dbc7906e2f970766b26771923a45","abstract_canon_sha256":"04f96fb3b131bb308fcfe6f3e6ceea65551b5862affa919929861f795bcbd049"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:57.879768Z","signature_b64":"WXJpDzjhiQmb6IObrTvhaTc9vXH/79gpL/nlSZzyTzxZ9tW0uqr1RxeSyGjO9zKeSSqlrVw/anCHo5xYZjryAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3780517be21246676ada2383f75ec835749e927a216ca0bb0ee41fba6c6bd7ba","last_reissued_at":"2026-05-17T23:41:57.879157Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:57.879157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"3-Lie algebra $A_{\\omega}^{\\delta}$-modules and induced modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Pei Liu, Ruipu Bai, Yue Ma","submitted_at":"2019-04-25T08:14:00Z","abstract_excerpt":"In this paper, we define the induced modules of Lie algebra ad$(B)$ associated with a 3-Lie algebra $B$-module, and study the relation between 3-Lie algebra $A_{\\omega}^{\\delta}$-modules and induced modules of inner derivation algebra ad$(A_{\\omega}^{\\delta})$. 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