Cotorsion Dimension of Weak Crossed Products

Abstract

Let $H$ be a finite-dimensional weak Hopf algebra over a field $k$ and $A$ an associative algebra, and $A\#_{\sigma}H$ a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of $A\#_{\sigma}H$ in terms of the corresponding data for $H$ and $A$.