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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Hopf algebras having a dense big cell
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by Julien Bichon and Simon Riche PDF
Trans. Amer. Math. Soc. 368 (2016), 515-538 Request permission

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 $\textrm {GL}$ and $\textrm {SL}$. 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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Additional Information
  • Julien Bichon
  • Affiliation: Laboratoire de Mathématiques (UMR 6620), CNRS, Université Blaise Pascal, Complexe universitaire des Cézeaux, 63171 Aubière Cedex, France
  • MR Author ID: 633469
  • 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
  • MR Author ID: 834430
  • Email: Simon.Riche@math.univ-bpclermont.fr
  • 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.
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 515-538
  • MSC (2010): Primary 20G42, 16T05
  • DOI: https://doi.org/10.1090/tran/6335
  • MathSciNet review: 3413872