4 papers
Hopf algebraic homogeneous spaces interpreted rationally: the Abe-Kanno theorem
Serge Skryabin
We present a Hopf algebraic generalization of the Abe-Kanno theorem on a correspondence between subgroups of an algebraic group and invariant subfields of the field of rational fun…
On Takeuchi's correspondence
Serge Skryabin
In this paper we review the Takeuchi correspondence between right coideal subalgebras and left -module factor coalgebras of a Hopf algebra with bijective antipode. We are especi…
Flatness over PI coideal subalgebras
Serge Skryabin
Under the assumption that a residually finite dimensional Hopf algebra H has an Artinian ring of fractions it is proved that H is a flat module over any right coideal subalgebra sa…
Flatness of Noetherian Hopf algebras over coideal subalgebras
Serge Skryabin
It is proved in the paper that a Noetherian residually finite dimensional Hopf algebra is a flat module over any right Noetherian right coideal subalgebra. In the case of Hopf suba…