6 papers
Triangular Poisson structures on Lie groups and symplectic reduction
Timothy J. Hodges, Milen Yakimov
We show that each triangular Poisson Lie group can be decomposed into Poisson submanifolds each of which is a quotient of a symplectic manifold. The Marsden-Weinstein-Meyer symplec…
The Double and Dual of a Quasitriangular Lie Bialgebra
Timothy J. Hodges, Milen Yakimov
Let G be a connected, simply connected Poisson-Lie group with quasitriangular Lie bialgebra g. An explicit description of the double D(g) is given, together with the embeddings of…
Quantization of certain skew-symmetric solutions of the classical Yang-Baxter equation
Robin Endelman, Timothy J. Hodges
An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of -matrices which generalize to higher dimensions the Jord…
Generating functions for the coefficients of the Cremmer-Gervais R-matrices
Timothy J. Hodges
The coefficients of certain operators on can be constructed using generating functions. Necessary and sufficient conditions are given for some such operators to satisf…
The Cremmer-Gervais solution of the Yang-Baxter equation
Timothy J. Hodges
A direct proof is given of the fact that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation.
Nonstandard solutions of the Yang-Baxter equation
Anthony Giaquinto, Timothy J. Hodges
Explicit solutions of the quantum Yang-Baxter equation are given corresponding to the non-unitary solutions of the classical Yang-Baxter equation for sl(5).