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arXiv · math/0610379

Bidynamical Poisson Groupoids

Romaric Pujol
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Abstract

We give relations between dynamical Poisson groupoids, classical dynamical Yang--Baxter equations and Lie quasi-bialgebras. We show that there is a correspondance between the class of bidynamical Lie quasi-bialgebras and the class of bidynamical Poisson groupoids. We give an explicit, analytical and canonical equivariant solution of the classical dynamical Yang--Baxter equation (classical dynamical $\ell$-matrices) when there exists a reductive decomposition $\g=ł\oplus\m$, and show that any other equivariant solution is formally gauge equivalent to the canonical one. We also describe the dual of the associated Poisson groupoid, and obtain the characterization that a dynamical Poisson groupoid has a dynamical dual if and only if there exists a reductive decomposition $\g=ł\oplus\m$.

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Romaric Pujol. 2006-10-11. Bidynamical Poisson Groupoids. https://arxiv.org/abs/math/0610379

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