The global dimensions of crossed products and crossed coproducts.
If \(H\) is a semisimple cosemisimple Hopf algebra, and \(A\#_\sigma H\) is a crossed product with invertible cocycle \(\sigma\), then it is shown that \(A\#_\sigma H\) and \(A\) have the same global dimension. This equality between global dimensions is also investigated when no semisimplicity of \(H\) or \(H^*\) are assumed, and the method of twistings is used to study the dual case of crossed coproducts of coalgebras.
scientific article; zbMATH DE number 5629541