Affine commutative-by-finite Hopf algebras

• DOI: 10.1016/j.jalgebra.2020.12.039
• Publication Date: 2021-01-14T23:49:15Z
• Authors: K.A. Brown; M. Couto
• Keywords: Algebraically closed field

The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and homological properties are recalled and classes of examples are listed. Bounds are obtained on the dimensions of simple $H$-modules, and the structure of $H$ is shown to be severely constrained when the finite dimensional extension is semisimple and cosemisimple.<br/>Preliminary version. Any comments are welcome<br/>