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Title: Quasitriangular and ribbon quasi-Hopf algebras
Authors: BULACU, Daniel
Issue Date: 2003
Source: COMMUNICATIONS IN ALGEBRA, 31(2). p. 657-672
Abstract: Following brinfeld (Drinfeld, V. G. (1990a). Quasi-Hopf algebras. Leningrad Math. J. 1:1419-1457) a quasi-Hopf algebra has, by definition, its antipode bijective. In this note, we will prove that for a quasitriangular quasi-Hopf algebra with an R-matrix R, this condition is unnecessary and also the condition of invertibility of R. Finally, we will give a characterization for a ribbon quasi-Hopf algebra. This characterization has already been given in Altschuler and Coste (Altschuler, D., Coste, A. (1992). Quasi-quantum groups, knots, three-manifolds and topological field theory. Comm. Math. Phys. 150:83-107.), but with an additional condition. We will prove that this condition is unnecessary.
Notes: Univ Bucharest, Fac Math, RO-70109 Bucharest 1, Romania. Limburgs Univ Ctr, Diepenbeek, Belgium.Bulacu, D, Univ Bucharest, Fac Math, Str Acad 14, RO-70109 Bucharest 1, Romania.
Keywords: quasi-Hopf algebra; R-matrix; antipode; ribbon element
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ISSN: 0092-7872
e-ISSN: 1532-4125
DOI: 10.1081/AGB-120017337
ISI #: 000182406900008
Category: A1
Type: Journal Contribution
Validations: ecoom 2004
Appears in Collections:Research publications

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