Rings graded equivalent to the Weyl algebra

Details Rings graded equivalent to the Weyl algebra Rings graded equivalent to the Weyl algebra

2007-11-09

arxiv.org/abs/0711.1494v2

Journal of Algebra 321 (2009), pp. 495-531

Mathematics

Rings and Algebras

38 pages; minor changes to final published version

Scientific paper

10.1016/j.jalgebra.2008.10.011

We consider the first Weyl algebra, A, in the Euler gradation, and completely classify graded rings B that are graded equivalent to A: that is, the categories gr-A and gr-B are equivalent. This includes some surprising examples: in particular, we show that A is graded equivalent to an idealizer in a localization of A. We obtain this classification as an application of a general Morita-type characterization of equivalences of graded module categories.

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