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Invariance of generalised Reynolds ideals under derived equivalences

Alexander Zimmermann
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Abstract

For any algebraically closed field $k$ of positive characteristic $p$ and any non negative integer $n$ Külshammer 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 Héthelyi, Horváth, Külshammer and Murray showed that this holds for Morita equivalent algebras.

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Alexander Zimmermann. 2006-03-29. Invariance of generalised Reynolds ideals under derived equivalences. https://arxiv.org/abs/math/0509580

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