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We prove that if C was hereditary, then the assignments V-> X_{V,ii} define algebra homomorphisms from the (dual) Hall-Ringel algebra of C to the P_{C,ii}, which generalize the well-known Feigin homomorphisms from the upper half of a quantum group to q-polynomial algebras.\n  If C is the representation ca"},"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":"1308.2992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-13T22:53:26Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"4b1834be2760c40a2d2b0009beb1b91f9ad20f92cad65ba6cb3ec6f1d5927d2f","abstract_canon_sha256":"3fda7a0e00018211638d802bc3f38b3b5bc538c49e879a1ae9e4d81566a1f884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:16.875535Z","signature_b64":"MjjcKGdwU79GBtUOKuz7EadLYXDJ/Fyie/JxCyO9WDG1e56YPvvZtPzCHth9rH83MdImtjzHXh7avakuDQb4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abf4ef0507ccd6bc63538dbb1a7cd7fd9cdcfd8d709baf5c18b22f0d700aa1c1","last_reissued_at":"2026-05-18T00:14:16.875016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:16.875016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum cluster characters of Hall algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Arkady Berenstein, Dylan Rupel","submitted_at":"2013-08-13T22:53:26Z","abstract_excerpt":"The aim of the present paper is to introduce a generalized quantum cluster character, which assigns to each object V of a finitary Abelian category C over a finite field FF_q and any sequence ii of simple objects in C the element X_{V,ii} of the corresponding algebra P_{C,ii} of q-polynomials. 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