On invariants of finite-dimensional pointed Hopf algebras (Q1280374)

The paper deals with the following problem. Let \(A\) be a commutative algebra. Prove that the extension \(A/A^H\) is integral (\(A^H\) is the subalgebra of invariants of the algebra \(A\)). A counterexample is constructed which contradicts the conjecture that the extension \(A/A^H\) is integral for any (not necessarily pointed) finite-dimensional Hopf algebra. Conditions are established under which the extension \(A/A^H\) is integral.