Hopf algebras having a dense big cell

Julien Bichon (1) , Simon Riche (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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-deformed quantum groups GL and SL. Here we examine the example of universal cosovereign Hopf algebras, for which the weight group is the free group on two generators.

Domaines: Algèbres quantiques [math.QA]; Théorie des représentations [math.RT]

Julien Bichon, Simon Riche. Hopf algebras having a dense big cell. Transactions of the American Mathematical Society, 2016, 368. ⟨hal-00843969v2⟩