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 , , for a pointed minimal quasitriangular Hopf algebra over a field 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 , is abelian. We show further that if is a quasitriangular Hopf algebra which is indecomposable as a coalgebra, then is contained in , the minimal quasitriangular Hopf algebra contained in . 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.

**[A]**E. Abe,*Hopf algebras*, Cambridge Univ. Press, Cambridge, 1980. MR**83a:16010****[K]**Kaplansky,*Bialgebras*, Lecture Notes in Math., University of Chicago, 1975. MR**55:8087****[M1]**S. Montgomery,*Hopf algebras and their actions on rings*, CBMS, Lecture Notes, vol. 82, Amer. Math. Soc., Providence, RI, 1993. MR**94i:16019****[M2]**------,*Indecomposable coalgebras, simple comodules, and pointed Hopf algebras*, (to appear).**[NZ]**W. D. Nicols and M. B. Zoller,*A Hopf algebra freeness theorem*, Amer. J. Math.**111**(1989), 381--385. MR**90c:16008****[R]**D. E. Radford*Minimal quasitriangular Hopf algebras*, J. Algebra**157**(1993), 281--315. MR**94c:16052****[ShM]**T. Shudo and H. Miyato,*On the decomposition of coalgebras*, Hiroshima J. Math.**8**(1978), 499--504. MR**80a:16018****[XF]**Y. H. Xu and Y. Fong,*On the decomposition of coalgebras*, Words, Languages and Combinatorics (Kyoto 1990), World Publishing, River Edge, NJ, 1992, pp.504--522. MR**93h:16070**

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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