Invariance of generalised Reynolds ideals under derived equivalences

Alexander Zimmermann (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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.

Mots clés: Reynolds ideal; derived equivalence

Domaines: Théorie des représentations [math.RT]

Alexander Zimmermann. Invariance of generalised Reynolds ideals under derived equivalences. 2006. ⟨hal-00009060v2⟩