Invariance of generalised Reynolds ideals under derived equivalences

Abstract

For any algebraically closed field $k$ of positive characteristic $p$ and any non negative integer $n$ Külshammer defined ideals $T\_n{A}^{\perp }$ 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 $T\_n{A}^{\perp }$ to $T\_n{B}^{\perp }$ for all $n$. Recently Héthelyi, Horváth, Külshammer and Murray showed that this holds for Morita equivalent algebras.