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To start with, all possible matched pairs between the two Taft algebras are described: if $\\bar{q} \\neq q^{n-1}$ then the matched pairs are in bijection with the group of $d$-th roots of unity in $k$, where $d = (m,\\,n)$ while if $\\bar{q} = q^{n-1}$ then besides the matched pairs above we obtain an additional family of matched pairs indexed by $k^{*}$. The corresponding bicrossed products (double cross product in Majid's terminology) are explicitly described by"},"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":"1603.01854","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-03-06T18:37:11Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"2df41c3c7c4e12545e5e5bda39e07605bfa82cdd813acc89483cb4ea70dc672d","abstract_canon_sha256":"8d03671426c6c67abb10f5af62b284a79635670200867ab02a0cc42dbc13ac3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:55.355236Z","signature_b64":"KwGrN68TTTWypVzfhw+JRWE4m//KuLm037iPz7J4BRnZYSuPY/3feiPT3FI9Y8nR6B6cponicQARfROfvP4PAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40e9562bc8878c73f17ea668bbfdf7d2cc0e8d5b0e579b548b609dd19ea79f18","last_reissued_at":"2026-05-18T00:27:55.354617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:55.354617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classifying bicrossed products of two Taft algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"A.L. Agore","submitted_at":"2016-03-06T18:37:11Z","abstract_excerpt":"We classify all Hopf algebras which factorize through two Taft algebras $\\mathbb{T}_{n^{2}}(\\bar{q})$ and respectively $T_{m^{2}}(q)$. To start with, all possible matched pairs between the two Taft algebras are described: if $\\bar{q} \\neq q^{n-1}$ then the matched pairs are in bijection with the group of $d$-th roots of unity in $k$, where $d = (m,\\,n)$ while if $\\bar{q} = q^{n-1}$ then besides the matched pairs above we obtain an additional family of matched pairs indexed by $k^{*}$. 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