Rings graded equivalent to the Weyl algebra

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Abstract / Description of output

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. Given a Z-graded ring R, an autoequivalence F of gr-R, and a finitely generated graded projective right R-module P, we show how to construct a twisted endomorphism ring EndRF(P) and prove:

Theorem. The Z-graded rings R and S are graded equivalent if and only if there are an autoequivalence F of gr-R and a finitely generated graded projective right R-module P such that the modules {FnP} generate gr-R andgenerate r-R S≅EndRF(P).

Original languageEnglish
Pages (from-to)495-531
Number of pages37
JournalInternational Electronic Journal of Algebra
Volume321
Issue number2
DOIs
Publication statusPublished - 15 Jan 2009

Keywords / Materials (for Non-textual outputs)

  • Graded Morita theory
  • Graded module category
  • Category equivalence
  • Weyl algebra
  • RIGHT IDEALS
  • MODULES

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