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Let $\\mathcal{A}^k$ be a vertex (super)algebra admitting a homomorphism $V^k(\\mathfrak{g},B)\\rightarrow \\mathcal{A}^k$. Under some technical conditions on $\\mathcal{A}^k$, we characterize the coset $\\text{Com}(V^k(\\mathfrak{g},B),\\mathcal{A}^k)$ for generic values of $k$. We establish the strong finite generation of this coset in full generali"},"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":"1407.8512","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-31T18:24:28Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"3cf3c571575140fb3b00a84c9178cbff048ebec97a044af6fc09cb35ee7248a5","abstract_canon_sha256":"26057a7620605a7f2a312e00b34d25b48c625c0a8283148972fc5c70795f3033"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:01:59.008613Z","signature_b64":"uXQHY2R15LRutwGrSeJdpp6g0N6tiMBJwq6SxEH2LZS73286NinW6zwROkB8VBWxpIj5Zn3AhlEbwLe3ew5dCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"672ac9b6d2ccafff9dc03d603b7eaaf7fa8b43a1821021ff9f2f546efa5824b6","last_reissued_at":"2026-07-05T01:01:59.008160Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:01:59.008160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cosets of affine vertex algebras inside larger structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Thomas Creutzig","submitted_at":"2014-07-31T18:24:28Z","abstract_excerpt":"Given a finite-dimensional reductive Lie algebra $\\mathfrak{g}$ equipped with a nondegenerate, invariant, symmetric bilinear form $B$, let $V^k(\\mathfrak{g},B)$ denote the universal affine vertex algebra associated to $\\mathfrak{g}$ and $B$ at level $k$. Let $\\mathcal{A}^k$ be a vertex (super)algebra admitting a homomorphism $V^k(\\mathfrak{g},B)\\rightarrow \\mathcal{A}^k$. Under some technical conditions on $\\mathcal{A}^k$, we characterize the coset $\\text{Com}(V^k(\\mathfrak{g},B),\\mathcal{A}^k)$ for generic values of $k$. 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