2018/03/15 by Sławomir Kapka, Kapka, Sławomir
Computer Science · Mathematics · #13N05 #13N15 #58J05 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1803.08452
openalex publication_date 2018/03/15 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28
We demonstrate a method of associating the principal symbol at a K-point\nwith a linear differential operator acting between modules over a commutative\nalgebra, and we use it to define the ellipticity of a linear differential\noperator in a purely algebraic way. We prove that the ellipticity is preserved\nby a surjective homomorphism of algebras. As an example, we show that for every\nreal affine variety there is an elliptic linear differential operator acting on\nthe algebra of regular functions on this variety.\n