Quasi-bialgebras and dynamical r-matrices

Details Quasi-bialgebras and dynamical r-matrices Quasi-bialgebras and dynamical r-matrices

2004-07-22

arxiv.org/abs/math/0407382v1

Mathematics

Quantum Algebra

latex 30 pages

Scientific paper

We study the relationship between general dynamical Poisson groupoids and Lie quasi-bialgebras. For a class of Lie quasi-bialgebras naturally compatible with a reductive decomposition, we extend the description of the moduli space of classical dynamical r-matrices of Etingof and Schiffmann. We construct, in each gauge orbit, an explicit analytic representative l. We translate the notion of duality for dynamical Poisson groupoids into a duality for Lie quasi-bialgebras. It is shown that duality maps the dynamical Poisson groupoid for l and a Lie quasi-bialgebra to the dynamical Poisson groupoid for the dual data.

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