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 language | English |
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Pages (from-to) | 495-531 |
Number of pages | 37 |
Journal | International Electronic Journal of Algebra |
Volume | 321 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Jan 2009 |
Keywords / Materials (for Non-textual outputs)
- Graded Morita theory
- Graded module category
- Category equivalence
- Weyl algebra
- RIGHT IDEALS
- MODULES