Hopf algebras having a dense big cell
Quantum Algebra
2013-12-04 v2 Representation Theory
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-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.
Cite
@article{arxiv.1307.3567,
title = {Hopf algebras having a dense big cell},
author = {Julien Bichon and Simon Riche},
journal= {arXiv preprint arXiv:1307.3567},
year = {2013}
}
Comments
v2: 20 pages. To appear in Trans. AMS