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Hopf algebras having a dense big cell


Authors: Julien Bichon and Simon Riche
Journal: Trans. Amer. Math. Soc. 368 (2016), 515-538
MSC (2010): Primary 20G42, 16T05
Published electronically: May 27, 2015
MathSciNet review: 3413872
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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 $ {\rm GL}$ and $ {\rm SL}$. Here we examine the example of universal cosovereign Hopf algebras, for which the weight group is the free group on two generators.


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Julien Bichon
Affiliation: Laboratoire de Mathématiques (UMR 6620), CNRS, Université Blaise Pascal, Complexe universitaire des Cézeaux, 63171 Aubière Cedex, France
Email: Julien.Bichon@math.univ-bpclermont.fr

Simon Riche
Affiliation: Laboratoire de Mathématiques (UMR 6620), CNRS, Université Blaise Pascal, Complexe universitaire des Cézeaux, 63171 Aubière Cedex, France
Email: Simon.Riche@math.univ-bpclermont.fr

DOI: https://doi.org/10.1090/tran/6335
Received by editor(s): July 18, 2013
Received by editor(s) in revised form: November 20, 2013
Published electronically: May 27, 2015
Additional Notes: The second author was supported by ANR Grants No. ANR-09-JCJC-0102-01 and No. ANR-2010-BLAN-110-02.
Article copyright: © Copyright 2015 American Mathematical Society