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This $64p^4$-dimensional Hopf algebra is a common double bosonization, $B(X^*)\\otimes B(X)\\otimes H$, of two rank-2 Nichols algebras $B(X)$ with fermionic generator(s), with $H=Z_{2p}\\otimes Z_{2p}$. The category of $\\bar{U}_q s\\ell(2|1)$-modules is equivalent to the category of Yetter--Drinfeld $B(X)$-modules in $C_{\\rho}={}^H_H\\!YD$, where coaction is defined by a universal $R$-matrix $\\rho$. As an application of the projective module construction, we find the associa"},"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":"1312.5127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-12-18T13:30:08Z","cross_cats_sorted":[],"title_canon_sha256":"dea431307171377fda1519190cc53110caa2a01eb974692314eebf27bccecad8","abstract_canon_sha256":"f8686a97ffa8c53a568bf24102d704c6fa83fc4564dcadc7be1e8df194745e65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:02.141363Z","signature_b64":"lbmI8XE5mBmb/kA9O2pH25ZCcnNAZfZ4UhzehHK2kRhZmOcaaA6SZdi1W/Yh9/1dYo0W5o0FD05/NDp2CFOpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b585689e9424aa72412aa102a444b7bf0cc0817ac7aa60e7fe19004bec42b3b","last_reissued_at":"2026-05-18T01:20:02.140564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:02.140564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations of $\\bar{U}_q s\\ell(2|1)$ at even roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"A M Semikhatov, I Yu Tipunin","submitted_at":"2013-12-18T13:30:08Z","abstract_excerpt":"We construct all projective modules of the restricted quantum group $\\bar{U}_q s\\ell(2|1)$ at an even, $2p$th, root of unity. 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