Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On double Poisson structures on commutative algebras   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.

35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th