If g is a quasitriangular Lie bialgebra, the formal Poisson group F[[g^*]] can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G = SL_2) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper.

Gavarini, F., Halbout, G. (2003). Braiding structures on formal Poisson groups and classical solutions of the QYBE. JOURNAL OF GEOMETRY AND PHYSICS, 46(3-4), 255-282 [10.1016/S0393-0440(02)00147-X].

Braiding structures on formal Poisson groups and classical solutions of the QYBE

GAVARINI, FABIO;
2003-06-01

Abstract

If g is a quasitriangular Lie bialgebra, the formal Poisson group F[[g^*]] can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G = SL_2) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper.
giu-2003
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Quantum groups; Quasitriangular Poisson groups; Quantum Yang–Baxter equation
http://www.sciencedirect.com/science/article/pii/S039304400200147X
Gavarini, F., Halbout, G. (2003). Braiding structures on formal Poisson groups and classical solutions of the QYBE. JOURNAL OF GEOMETRY AND PHYSICS, 46(3-4), 255-282 [10.1016/S0393-0440(02)00147-X].
Gavarini, F; Halbout, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/19095
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