Vol. 8, No. 5, 2014

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Poisson structures and star products on quasimodular forms

François Dumas and Emmanuel Royer

Vol. 8 (2014), No. 5, 1127–1149
Abstract

We construct and classify all Poisson structures on quasimodular forms that extend the one coming from the first Rankin–Cohen bracket on the modular forms. We use them to build formal deformations on the algebra of quasimodular forms.

Keywords
quasimodular forms, Poisson brackets, Rankin–Cohen brackets, formal deformation, Eholzer product, star product
Mathematical Subject Classification 2010
Primary: 17B63
Secondary: 11F25, 11F11, 16W25
Milestones
Received: 26 July 2013
Revised: 20 January 2014
Accepted: 24 March 2014
Published: 16 September 2014
Authors
François Dumas
Clermont Université
Université Blaise Pascal
Laboratoire de mathématiques
BP 10448
F-63000 Clermont-Ferrand
France
Université Blaise Pascal
Laboratoire de mathématiques
Les Cézeaux
BP 80026
F-63171 Aubière
France
Emmanuel Royer
Clermont Université
Université Blaise Pascal
Laboratoire de mathématiques
BP 10448
F-63000 Clermont-Ferrand
France
Université Blaise Pascal
Laboratoire de mathématiques
Les Cézeaux
BP 80026
F-63171 Aubière
France