Two properties of endomorphisms of Weyl algebras

2015/08/11 by Niels Lauritzen, Lauritzen, Niels, Jesper Funch Thomsen +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.AG #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.1508.02499

arxiv created 2015/08/11 · arxiv updated 2015/08/12

Abstract

We show that endomorphisms of Weyl algebras over fields of characteristic zero are flat and that birational endomorphisms are automorphisms by reducing to positive characteristic. We also give examples showing that endomorphisms of Weyl algebras are not in general flat over fields of positive characteristic.

Related

• The starred Dixmier's conjecture
• Finitely generated bimodules over Weyl algebras
• The Conjecture of Dixmier for the first Weyl algebra is true
• About Dixmier's conjecture
• The starred Dixmier conjecture for A₁