Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems

Fairon, M. (2022) Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems. Annales Henri Lebesgue, 5, pp. 179-262. (doi: 10.5802/ahl.121)

Abstract

Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket. In this work, we provide a study of morphisms of double (quasi-)Poisson algebras, which we relate to the H0-Poisson structures of Crawley-Boevey. We prove in particular that the double (quasi-)Poisson algebra structure defined by Van den Bergh for an arbitrary quiver only depends upon the quiver seen as an undirected graph, up to isomorphism. We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.

• Item Type: Articles
• Additional Information: This research was supported by a Rankin-Sneddon Research Fellowship of the University of Glasgow.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fairon, Dr Maxime
• Authors: Fairon, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Annales Henri Lebesgue
• Publisher: Universite de Rennes 1 Institut de Recherche Mathématique de Rennes
• ISSN: 2644-9463
• ISSN (Online): 2644-9463

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