Endomorphism rings of \(H\)-comodule algebras
Let \(A/B\) be a (left) Hopf-Galois extension with Hopf algebra \(H\). For a (left) coideal subalgebra \(K\subset H\) let \(A(K)\subseteq A\) be the cotensor product of \(A\) with \(K\) over \(H\). The authors study the rings \(A\otimes_{A(K)} A\) and \(\text{End}_{A(K)}(A)\) under suitable flatness conditions and find interesting relations with smash products and crossed products. These results generalize known theorems for group graded rings. Similar results are obtained for the right hand side and a Hopf subalgebra \(L\subseteq H\).
scientific article; zbMATH DE number 885633