{"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$(A_{\\omega}^{\\delta})$. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11196","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"}