Separating invariants for Hopf algebras of small dimensions (Q2191305)

In the paper under review the problem of consruction of invariants separating finite-dimensional Hopf algebras is considered. Fix a base in the vector space underlying a Hopf algebra then the Hopf algebra structures can be represented by their associated structure constants. These constants form a closed subvariety. The general linear group GL\(_n\) acts on the \(n\)-dimensional vector space by change of basis then induces an action also on the associated closed subvariety. This action induces an action on the subvariety constructed above. The orbits of this action correspond to isomorphism classes. ``They show in [\textit{S. Datt} et al., Math. Res. Lett. 10, No. 5--6, 571--586 (2003; Zbl 1075.16017)] that the generators of the ring of invariants corresponding to this action on the closed subvariety give a collection of polynomials which separate isomorphism classes of semi-simple Hopf algebras of dimension \(n\).'' In the paper under review the authors ``extend this result to finite dimensional Hopf algebras of certain dimensions.''