A stochastic Poisson structure associated to a Yang-Baxter equation

We consider a simple solution of a Yang-Baxter equation on loop algebra and deduce from it a Sklyanin Poisson structure which operates continuously on a Sobolev test algebra on the Wiener space of the Lie algebra.

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 343; no. 1; pp. 12066 - 4
Main Author Leandre, Remi
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.01.2012
Subjects
Algebra
Lie groups
Mathematical analysis
Metric space
Physics
Stochasticity
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Summary:We consider a simple solution of a Yang-Baxter equation on loop algebra and deduce from it a Sklyanin Poisson structure which operates continuously on a Sobolev test algebra on the Wiener space of the Lie algebra.
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ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/343/1/012066