Bidynamical Poisson Groupoids

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dc.creatorPujol, Romaric
dc.date2006-10-11
dc.date.accessioned2026-07-07T07:28:58Z
dc.date.available2026-07-07T07:28:58Z
dc.descriptionWe 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 $\g=ł\oplus\m$.
dc.descriptionLaTeX, 22 pages
dc.identifierhttps://arxiv.org/abs/math/0610379
dc.identifierhttp://arxiv.org/abs/math/0610379
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117931
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject17B62; 53D17; 58H05; 35Q99
dc.titleBidynamical Poisson Groupoids
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