2011/01/06 by Jason P. Bell, Bell, Jason P., Agata Smoktunowicz +1
Mathematics · #16P90 #16S32 #16S38 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Rings and Algebras (math.RA) #math.RA #msc:16P90 #msc:16S32 #msc:16S38
paper · pdf · doi:10.48550/arxiv.1101.1123
10 pages
openalex publication_date 2011/01/06 · arxiv created 2011/01/16 · arxiv updated 2011/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 D(X), the ring of differential operators on an irreducible smooth affine curve X, and A is birationally isomorphic to D(X).