arXiv subjects
Publications and source records attributed to S. Skryabin.
This text is the English translation of a 1986 manuscript which gives the classification of the differential forms parametrizing the finite-dimensional Lie algebras of hamiltonian and contact Cartan types over fields of positive characteristic. The results of this paper have not been previously published in full.
Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H,A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras, and the latter are Frobenius algebras. Similar results are obtained for H-simple H-module algebras.
Some new results on the module structure of Hopf algebras over a certain class of Hopf subalgebras and right coideal subalgebras are proved.
This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.
We investigate the transformed Hopf algebras in Hopf Galois extensions. The final goal of this paper is to introduce certain triangular Hopf algebras associated with restricted Frobenius Lie algebras over a field of characteristic $p>0$.
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.