Hopf quivers and Nichols algebras in positive characteristic
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- by Claude Cibils, Aaron Lauve and Sarah Witherspoon
- Proc. Amer. Math. Soc. 137 (2009), 4029-4041
- DOI: https://doi.org/10.1090/S0002-9939-09-10001-1
- Published electronically: July 23, 2009
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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.References
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Bibliographic Information
- Claude Cibils
- Affiliation: Institut de Mathématiques et de Modélisation de Montpellier, Université Montpellier 2, F-34095 Montpellier Cedex 5, France
- MR Author ID: 49360
- ORCID: 0000-0003-3269-9525
- Email: Claude.Cibils@math.univ-montp2.fr
- Aaron Lauve
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- MR Author ID: 680048
- Email: lauve@math.tamu.edu
- Sarah Witherspoon
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- MR Author ID: 364426
- Email: sjw@math.tamu.edu
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 4029-4041
- MSC (2000): Primary 16W30
- DOI: https://doi.org/10.1090/S0002-9939-09-10001-1
- MathSciNet review: 2538564