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- W2951009675 abstract "The Weyl algebra over a field $k$ of characteristic $0$ is a simple ring of Gelfand-Kirillov dimension 2, which has a grading by the group of integers. We classify all $mathbb{Z}$-graded simple rings of GK-dimension 2 and show that they are graded Morita equivalent to generalized Weyl algebras as defined by Bavula. More generally, we study $mathbb{Z}$-graded simple rings $A$ of any dimension which have a graded quotient ring of the form $K[t, t^{-1}; sigma]$ for a field $K$. Under some further hypotheses, we classify all such $A$ in terms of a new construction of simple rings which we introduce in this paper. In the important special case that $operatorname{GKdim} A = operatorname{tr.deg}(K/k) + 1$, we show that $K$ and $sigma$ must be of a very special form. The new simple rings we define should warrant further study from the perspective of noncommutative geometry." @default.
- W2951009675 created "2019-06-27" @default.
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- W2951009675 date "2013-10-20" @default.
- W2951009675 modified "2023-10-16" @default.
- W2951009675 title "$mathbb{Z}$-graded simple rings" @default.
- W2951009675 cites W2154008761 @default.
- W2951009675 doi "https://doi.org/10.48550/arxiv.1310.5406" @default.
- W2951009675 hasPublicationYear "2013" @default.
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