{"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01461","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}