Geometric perspective on Nichols algebras

We formulate the generation of finite dimensional pointed Hopf algebras by group-like elements and skew-primitives in geometric terms. This is done through a more general study connected coconnected inside braided fusion category C. describe such as orbits for action reductive group on an affine variety. then show that closed are precisely Nichols algebras, all other therefore deformations algebras. For case where C YDGG Yetter-Drinfeld modules over G, this reduces question to about rigidity orbits. Comparing results Angiono Kochetov Mastnak, gives new proof with abelian groups elements. if V simple object B(V) dimensional, must be rigid. also non-rigid algebra can always deformed pre-Nichols or post-Nichols which isomorphic