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arXiv · 1603.07553

On double Poisson structures on commutative algebras

Geoffrey Powell
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Abstract

Double Poisson structures (a la Van den Bergh) on commutative algebras are studied; the main result shows that there are no non-trivial such structures on polynomial algebras of Krull dimension greater than one. For a general commutative algebra A, 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.

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Geoffrey Powell. 2016-03-24. On double Poisson structures on commutative algebras. https://doi.org/10.1016/j.geomphys.2016.07.003

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