On a question of Rickard on tensor product of stably equivalent algebras

الأصل · EN

Let _p be the algebraic closure of the prime field of characteristic p. After observing that the principal block B of _pPSU(3,pʳ) 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 pʳ∈{3,4,5,8}. As a consequence, the algebra B⊗__p _p[X]/Xᵖ is not stably equivalent of Morita type to b⊗__p_p[X]/Xᵖ in these cases. This yields a negative answer to a question of Rickard.