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Article Dans Une Revue Experimental Mathematics Année : 2017

On a Question of Rickard on Tensor Products of Stably Equivalent Algebras

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Résumé

Let r be a positive integer, let p be a prime, and denote an algebraic closure of the prime field . After observing that the principal block B of is stably equivalent of Morita type to its Brauer correspondent b, we compute the radical series of the center Z(b), and, using GAP, the radical series of Z(B) in the cases p(r) \3, 4, 5, 7, 8\. In these cases, the dimensions of the last nonzero power of the radical of Z(b) and Z(B) are different, and it follows that the algebra is not stably equivalent of Morita type to . This yields a negative answer to a question of Rickard.
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Dates et versions

hal-03621753 , version 1 (28-03-2022)

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Serge Bouc, Alexander Zimmermann. On a Question of Rickard on Tensor Products of Stably Equivalent Algebras. Experimental Mathematics, 2017, 26 (1), pp.31-44. ⟨10.1080/10586458.2015.1107869⟩. ⟨hal-03621753⟩
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