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

Serge Bouc, Alexander Zimmermann

Published 2015-01-07Version 1

Let F be the algebraic closure of the prime field of characteristic p. After observing that the principal block B of F PSU (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) $\in$ {(2, 2), (3, 1), (5, 1)}. As a consequence, the algebra B $\otimes$ F[X]/X^p is not stably equivalent of Morita type to b $\otimes$ F[X]/X^p in these cases. This yields a negative answer to a question of Rickard.