Abstract
AbstractWe exhibit new examples of double quasi-Poisson brackets, based on some classification results and the method of fusion. This method was introduced by Van den Bergh for a large class of double quasi-Poisson brackets which are said differential, and our main result is that it can be extended to arbitrary double quasi-Poisson brackets. We also provide an alternative construction for the double quasi-Poisson brackets of Van den Bergh associated to quivers, and of Massuyeau–Turaev associated to the fundamental groups of surfaces.
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Alekseev, A., Kawazumi, N., Kuno, Y., Naef, F.: The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem. Adv. Math. 326, 1–53 (2018). arXiv:1703.05813
2. Alekseev, A., Kawazumi, N., Kuno, Y., Naef, F.: The Goldman-Turaev Lie bialgebras and the Kashiwara-Vergne problem in higher genera. Preprint; arXiv:1804.09566
3. Alekseev, A., Kosmann-Schwarzbach, Y., Meinrenken, E.: Quasi-Poisson manifolds. Canad. J. Math. 54(1), 3–29 (2002). arXiv:math/0006168
4. Bielawski, R.: Quivers and Poisson structures. Manuscripta Math. 141(1-2), 29–49 (2013). arXiv:1108.3222
5. Crawley-Boevey, W.: Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities. Comment. Math. Helv. 74(4), 548–574 (1999)
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