Gorenstein injective and projective modules and actions of finite-dimensional Hopf algebras. (Q950722)

Let \(H\) be a finite dimensional Hopf algebra over a field \(k\), let \(A\) be a left \(H\)-module algebra and \(B=A^{co\,H}\) the algebra of coinvariants. In this paper, the author considers the problem of preserving properties of covers between the categories of modules over \(A\), \(B\) and the smash product \(A\#H\). These results extend the graded case by \textit{M. J. Asensio}, the author and the reviewer [J. Algebra 215, No. 2, 437-459 (1999; Zbl 0942.16049)]. In the last section, as consequence of the previous results, new examples of Gorenstein categories, as defined by \textit{E. Enochs, S. Estrada} and \textit{J. R. García-Rozas} [in Math. Nachr. 281, No. 4, 525-540 (2008; Zbl 1146.18004)], are presented.