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In addition they commute when p=q^{2k} for k integer non-zero, and they belong to the center of ${\\cal A}_{q,p}({\\hat sl}(2)_c)$ when k is odd. The Poisson structures obtained for t(z) in these classical limits are identical to the q-deformed Virasoro Poisson algebra, characterizing the exchange algebras at generic values of p, q and m as new ${\\cal W}_{q,p}(sl(2))$ algebras."},"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":"q-alg/9706013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-06-13T12:21:34Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"7434b0094f0d31709d03576a0307d66388cdea7f64c3ede738e926518328dde5","abstract_canon_sha256":"1aedf4c1a1c1a1ce20a473a3b70b683e24843f41fa63f4656478446679d09d1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:06:26.956039Z","signature_b64":"p5+WHiOK0dGpyFpcrAGGGYhdd+sI9y3C4sdQfsHKW7ixpiSSyeXYbGecGCdyzd9PDsBEAxGySqU+gFoHLRLlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abc47b00524be98af9903884e01c68055e1240e669b6ad7850170add52fbe755","last_reissued_at":"2026-07-04T16:06:26.955650Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:06:26.955650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New ${\\cal W}_{q,p}(sl(2))$ algebras from the elliptic algebra ${\\cal A}_{q,p}({\\hat sl}(2)_c)$","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"J. 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