TY - JOUR

T1 - Quasitriangular hopf algebras whose group-like elements form an abelian group

AU - Westreich, Sara

PY - 1996

Y1 - 1996

N2 - 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 AR, 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.

AB - 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 AR, 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.

UR - http://www.scopus.com/inward/record.url?scp=33645945281&partnerID=8YFLogxK

U2 - 10.1090/s0002-9939-96-03110-3

DO - 10.1090/s0002-9939-96-03110-3

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AN - SCOPUS:33645945281

SN - 0002-9939

VL - 124

SP - 1023

EP - 1026

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -