Normal forms for ordinary differential operators, II
Algebraic Geometry
2025-11-10 v1 Mathematical Physics
math.MP
Quantum Algebra
Rings and Algebras
Abstract
In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for operators in the Weyl algebra or, more generally, in the ring of ordinary differential operators, which we prove in the case when operators have a normal form with the restriction top line (for details see Introduction).
Cite
@article{arxiv.2511.05117,
title = {Normal forms for ordinary differential operators, II},
author = {J. Guo and A. B. Zheglov},
journal= {arXiv preprint arXiv:2511.05117},
year = {2025}
}
Comments
This is part 2 of a split version, to appear in Izvestiya: Mathematics. For part 1, see arXiv:2406.14414v4. For part 3 see arXiv:2506.19799v2