{"paper":{"title":"Universal two-parameter even spin $\\mathcal{W}_{\\infty}$-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Shashank Kanade","submitted_at":"2018-05-25T17:26:14Z","abstract_excerpt":"We construct the unique two-parameter vertex algebra which is freely generated of type ${\\mathcal W}(2,4,6,\\dots)$, and generated by the weights $2$ and $4$ fields. Subject to some mild constraints, all vertex algebras of type ${\\mathcal W}(2,4,\\dots, 2N)$ for some $N$, can be obtained as quotients of this universal algebra. This includes the $B$ and $C$ type principal ${\\mathcal W}$-algebras, the $\\mathbb{Z}_2$-orbifolds of the $D$ type principal ${\\mathcal W}$-algebras, and many others which arise as cosets of affine vertex algebras inside larger structures. As an application, we classify al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11031","kind":"arxiv","version":6},"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/1805.11031/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"}