Title: On a question of Rickard on tensor product of stably equivalent algebras
Authors: Serge Bouc and Alexander Zimmermann

Abstract: 
Let r be a positive integer, let p be a prime and F denote an algebraic closure of the prime field F_p. After observing that the principal block B of FPSU(3,p^r) 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 = 3,4,5,8. In these cases, the dimensions of the last non zero power of the radical of Z(b) and Z(B) are different, and it follows that the algebra B\otimes_F F[X]/X^p is not stably equivalent of Morita type to b\otimes_F F[X]/X^p. This yields a negative answer to a question of Rickard.