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Journal Articles Journal of Geometry and Physics Year : 2016

On double Poisson structures on commutative algebras

Abstract

Double Poisson structures (à la Van den Bergh) on commutative algebras are considered. The main result shows that there are no non-trivial such structures on polynomial algebras of Krull dimension greater than one. For an arbitrary commutative algebra AA, this places significant restrictions on possible double Poisson structures. Exotic double Poisson structures are exhibited by the case of the polynomial algebra on a single generator, previously considered by Van den Bergh.

Dates and versions

hal-01392731 , version 1 (04-11-2016)

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Geoffrey Powell. On double Poisson structures on commutative algebras. Journal of Geometry and Physics, 2016, 110, pp.1-8. ⟨10.1016/j.geomphys.2016.07.003⟩. ⟨hal-01392731⟩
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