2023/08/18 by Lauritzen, Niels, Thomsen, Jesper Funch
#14A22 #14R10 #16H05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2308.09384
Let A be the n-th Weyl algebra over a field of characteristic zero, and φ:A→ A an endomorphism with S = φ(A). We prove that if A is finitely generated as a left or right S-module, then S = A. The proof involves reduction to large positive characteristics. By holonomicity, A is always finitely generated as an S-bimodule. Moreover, if this bimodule property could be transferred into a similar property in large positive characteristics, then we could again conclude that A=S. The latter would imply the Dixmier Conjecture.