Quasitriangular and Ribbon Quasi-Hopf Algebras
Quasitriangular and Ribbon Quasi-Hopf Algebras
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DOI：
10.1081/agb-120017337
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发表时间：
2003-01
影响因子：
0.7
通讯作者：
D. Bulacu;E. Nauwelaerts
中科院分区：
文献类型：
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作者：
D. Bulacu;E. Nauwelaerts
摘要如下（Drinfeld，V. G.（1990年a）。Quasi-Hopf algebras.Leningrad Math.J.1：1419-1457）根据定义，一个拟霍普夫代数有它的对极双射。本文证明了对于具有R-矩阵R的拟三角拟Hopf代数，这个条件是不必要的，也是R可逆的条件。最后，我们给出了带拟Hopf代数的一个刻画。这种表征已经在Altschloven和Coste（Altschloven，D.，Coste，A.（1992年）。准量子群、纽结、三流形与拓扑场论。150：83-107.），但有一个附加条件我们将证明这个条件是不必要的。
Abstract Following (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.