Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898388 | Journal of Geometry and Physics | 2016 | 8 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Geoffrey Powell,