The noetherian properties of the rings of differential operators on central 2-arrangements

Details The noetherian properties of the rings of differential operators on central 2-arrangements The noetherian properties of the rings of differential operators on central 2-arrangements

2011-06-09

arxiv.org/abs/1106.1756v1

Mathematics

Rings and Algebras

Scientific paper

Whereas Holm proved that the ring of differential operators on a generic hyperplane arrangement is finitely generated as an algebra, the problem of its Noetherian properties is still open. In this article, after proving that the ring of differential operators on a central arrangement is right Noetherian if and only if it is left Noetherian, we prove that the ring of differential operators on a central 2-arrangement is Noetherian. In addition, we prove that its graded ring associated to the order filtration is not Noetherian when the number of the consistuent hyperplanes is greater than 1.

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