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PACIFIC JOURNAL OF MATHEMATICS,Vol. 192, No. 2, 2000, 28 pages

Abstract:

The paper defines braided Lie bialgebras as the infinitesimal version of braided groups. It consists of a Lie algebra 'b' equipped with additional structure. (Previously, Drinfeld introduced Lie bialgebras as the infinitesimal dual of quantum groups.). The theorems proven in Section 3 connect braided-Lie bialgebras with quasitriangular Lie bialgebras. The simplest example is that with zero braided-Lie cobracket as the infinitesimal versions of the q-affine plane braided groups. "In principle one could also formulate an abstract notion of `infinitesimal braiding' as a Lie version of a general braided category", but this problem is not addressed in this paper. Free download online at: http://nyjm.albany.edu:8000/PacJ/p/2000/192-2-10.pdf

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