INVARIANCE OF GENERALISED REYNOLDS IDEALS UNDER DERIVED EQUIVALENCES

Abstract

For any algebraically closed field $k$ of positive characteristic $p$ and any non negative integer $n$ K\ulshammer defined ideals $T\_nA^\perp$ of the centre of a symmetric $k$-algebra $A$. We show that for derived equivalent algebras $A$ and $B$ there is an isomorphism of the centres of $A$ and $B$ mapping $T\_nA^\perp$ to $T\_nB^\perp$ for all $n$. Recently H\'ethelyi, Horv\'ath, K\ulshammer and Murray showed that this holds for Morita equivalent algebras.