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Quasi-bialgebras and dynamical r-matrices

Serge Parmentier·Romaric Pujol
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Abstract

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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Serge Parmentier, Romaric Pujol. 2004-07-22. Quasi-bialgebras and dynamical r-matrices. https://arxiv.org/abs/math/0407382

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