{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:I6IIKSMIKUHY2V3YZYJQ5IG4JE","short_pith_number":"pith:I6IIKSMI","schema_version":"1.0","canonical_sha256":"4790854988550f8d5778ce130ea0dc490a28f28b51b44eea82c1c181d1cd75a4","source":{"kind":"arxiv","id":"1501.01461","version":3},"attestation_state":"computed","paper":{"title":"On a question of Rickard on tensor product of stably equivalent algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA","math.RT"],"primary_cat":"math.GR","authors_text":"Alexander Zimmermann (LAMFA), Serge Bouc (LAMFA)","submitted_at":"2015-01-07T12:18:05Z","abstract_excerpt":"Let $\\overline\\F\\_p$ be the algebraic closure of the prime field of characteristic $p$. After observing that the principal block $B$ of $\\overline\\F\\_pPSU(3,p^r)$ is stably equivalent of Morita type to its Brauer correspondent $b$, we show however that the centre of $B$ is not isomorphic as an algebra to the centre of $b$ in the cases $p^r\\in\\{3,4,5,8\\}$. As a consequence, the algebra $B\\otimes\\_{\\overline{\\F}\\_p}\\overline \\F\\_p[X]/X^p$ is not stably equivalent of Morita type to $b\\otimes\\_{\\overline\\F\\_p}\\overline\\F\\_p[X]/X^p$ in these cases. This yields a negative answer to a question of Ric"},"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":"1501.01461","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-07T12:18:05Z","cross_cats_sorted":["math.CT","math.RA","math.RT"],"title_canon_sha256":"d0862b8c100e4a01bc72f3389580ce409f58e0e38b0e56eda5f2a05323ddd6ac","abstract_canon_sha256":"94219d76d46132dd4e852579b8c2039a8f24868f563f50ffe13681a8174d01e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:56.790181Z","signature_b64":"NXzpvevbTm1NFSfgmJPdiEZY1XjUJzuetgauS+WsT0xnbTEEoxHMNVLaVemkbUilwt1McSMywMs+qN1ZahuyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4790854988550f8d5778ce130ea0dc490a28f28b51b44eea82c1c181d1cd75a4","last_reissued_at":"2026-05-18T02:27:56.789786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:56.789786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a question of Rickard on tensor product of stably equivalent algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA","math.RT"],"primary_cat":"math.GR","authors_text":"Alexander Zimmermann (LAMFA), Serge Bouc (LAMFA)","submitted_at":"2015-01-07T12:18:05Z","abstract_excerpt":"Let $\\overline\\F\\_p$ be the algebraic closure of the prime field of characteristic $p$. After observing that the principal block $B$ of $\\overline\\F\\_pPSU(3,p^r)$ is stably equivalent of Morita type to its Brauer correspondent $b$, we show however that the centre of $B$ is not isomorphic as an algebra to the centre of $b$ in the cases $p^r\\in\\{3,4,5,8\\}$. As a consequence, the algebra $B\\otimes\\_{\\overline{\\F}\\_p}\\overline \\F\\_p[X]/X^p$ is not stably equivalent of Morita type to $b\\otimes\\_{\\overline\\F\\_p}\\overline\\F\\_p[X]/X^p$ in these cases. 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