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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hopf quivers and Nichols algebras in positive characteristic


Authors: Claude Cibils, Aaron Lauve and Sarah Witherspoon
Journal: Proc. Amer. Math. Soc. 137 (2009), 4029-4041
MSC (2000): Primary 16W30
Published electronically: July 23, 2009
MathSciNet review: 2538564
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Abstract: We apply a combinatorial formula of the first author and Rosso for products in Hopf quiver algebras to determine the structure of Nichols algebras. We illustrate this technique by explicitly constructing new examples of Nichols algebras in positive characteristic. We further describe the corresponding Radford biproducts and some liftings of these biproducts, which are new finite-dimensional pointed Hopf algebras.


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Additional Information

Claude Cibils
Affiliation: Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier 2, F-34095 Montpellier Cedex 5, France
Email: Claude.Cibils@math.univ-montp2.fr

Aaron Lauve
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: lauve@math.tamu.edu

Sarah Witherspoon
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: sjw@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10001-1
PII: S 0002-9939(09)10001-1
Received by editor(s): January 23, 2009
Received by editor(s) in revised form: April 13, 2009
Published electronically: July 23, 2009
Additional Notes: The second and third authors were partially supported by Texas Advanced Research Program Grant #010366-0046-2007.
The third author was partially supported by NSA grant H98230-07-1-0038 and NSF grant DMS-0800832.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2009 American Mathematical Society