Gelfand-Kirillov dimension of cosemisimple Hopf algebras

Abstract

In this note, we compute the Gelfand-Kirillov dimension of cosemisimple Hopf algebras that arise as deformations of a linearly reductive algebraic group. Our work lies in a purely algebraic setting and generalizes results of Goodearl-Zhang (2007), of Banica-Vergnioux (2009), and of D'Andrea-Pinzari-Rossi (2017).

6 pages + references ; small changes following referee comments ; to appear in Proc. AMS