Bidynamical Poisson Groupoids

Details Bidynamical Poisson Groupoids Bidynamical Poisson Groupoids

2006-10-11

arxiv.org/abs/math/0610379v1

Mathematics

Quantum Algebra

LaTeX, 22 pages

Scientific paper

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 $\g=\l\oplus\m$, 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 $\g=\l\oplus\m$.

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