Geometric perspective on Nichols algebras (Q2122229)

In this paper, the author gives a formulation of the generation of finite dimensional pointed Hopf algebras by group-like elements and skew-primitives in geometric terms, by describing such Hopf algebras as orbits for the action of a reductive group on an affine variety. It is shown that the closed orbits are precisely the orbits of Nichols algebras, and that all other algebras are therefore deformations of Nichols algebras. This reduces the question of generation by group-like elements and skew-primitives to a geometric question about rigidity of orbits. Several applications to the study of deformations of finite dimensional Nichols algebras are discussed.