Forms of pointed Hopf algebras
The authors classify finite dimensional Hopf algebras over a field \(k\) of characteristic \(0\) which are forms of certain pointed Hopf algebras over the algebraic closure \(\overline k\). The classes of pointed Hopf algebras whose forms are determined are those of dimension \(p^2\), \(p^3\) (\(p\) an odd prime number) and Frobenius-Lusztig kernels; it is assumed that the field \(k\) contains a suitable root of \(1\), so that suitable ``split'' forms do exist. The description of the forms is parallel to descriptions of forms of other algebraic objects.
scientific article; zbMATH DE number 1355505