Hopf algebras having a dense big cell

Abstract

We discuss some axioms that ensure that a Hopf algebra has its simple comodules classified using an analogue of the Borel–Weil construction. More precisely we show that a Hopf algebra having a dense big cell satisfies the above requirement. This method has its roots in the work of Parshall and Wang in the case of q q -deformed quantum groups GL \textrm {GL} and SL \textrm {SL} . Here we examine the example of universal cosovereign Hopf algebras, for which the weight group is the free group on two generators.