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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quasitriangular Hopf algebras whose group-like
elements form an abelian group


Author: Sara Westreich
Journal: Proc. Amer. Math. Soc. 124 (1996), 1023-1026
MSC (1991): Primary 16W30
DOI: https://doi.org/10.1090/S0002-9939-96-03110-3
MathSciNet review: 1301534
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Abstract: In this paper we prove some properties of the set of group-like elements of $A$, $G(A)$, for a pointed minimal quasitriangular Hopf algebra $A$ over a field $k$ of characteristic 0, and for a pointed quasitriangular Hopf algebra which is indecomposable as a coalgebra. We first show that over a field of characteristic 0, for any pointed minimal quasitriangular Hopf algebra $A$, $G(A)$ is abelian. We show further that if $A$ is a quasitriangular Hopf algebra which is indecomposable as a coalgebra, then $G(A)$ is contained in $A_R$, the minimal quasitriangular Hopf algebra contained in $A$. As a result, one gets that over a field of characteristic 0, a pointed indecomposable quasitriangular Hopf algebra has a finite abelian group of group-like elements.


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Additional Information

Sara Westreich
Affiliation: Interdisciplinary Department of Social Sciences, Bar-Ilan University, 52 900 Ramat-Gan, Israel
Email: sarawest@shekel.ec.biu.ac.il

DOI: https://doi.org/10.1090/S0002-9939-96-03110-3
Received by editor(s): March 14, 1994
Received by editor(s) in revised form: September 12, 1994
Additional Notes: Partially supported by Basic Research Foundation, administrated by the Israel Academy of Sciences and Humanities, while the author was visiting at Ben-Gurion University.
Communicated by: Lance W. Small
Article copyright: © Copyright 1996 American Mathematical Society