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)
Text
252171.pdf - Published Version Available under License Creative Commons Attribution. 976kB |
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 |
Copyright Holders: | Copyright © 2022 The Author |
First Published: | First published in Annales Henri Lebesgue 5: 179-262 |
Publisher Policy: | Reproduced under a Creative Commons License |
Related URLs: |
University Staff: Request a correction | Enlighten Editors: Update this record