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Rings of differential operators on curves
- Publication Year :
- 2011
-
Abstract
- Let $k$ be an algebraically closed field of characteristic 0 and let $A$ be a finitely generated $k$-algebra that is a domain whose Gelfand-Kirillov dimension is in $[2,3)$. We show that if $A$ has a nonzero locally nilpotent derivation then $A$ has quadratic growth. In addition to this, we show that $A$ either satisfies a polynomial identity or $A$ is isomorphic to a subalgebra of $\mathcal{D}(X)$, the ring of differential operators on an irreducible smooth affine curve $X$, and $A$ is birationally isomorphic to $\mathcal{D}(X)$.<br />Comment: 10 pages
- Subjects :
- Mathematics - Rings and Algebras
16P90, 16S32, 16S38
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1101.1123
- Document Type :
- Working Paper