Mad Subalgebras of Rings of Differential Operators on Curves
Quantum Algebra
2007-05-23 v3 Representation Theory
Abstract
We study the maximal abelian ad-nilpotent (mad) subalgebras of the domains D Morita equivalent to the first Weyl algebra. We give a complete description both of the individual mad subalgebras and of the space of all such. A surprising consequence is that this last space is independent of D. Our results generalize some classic theorems of Dixmier about the Weyl algebra.
Cite
@article{arxiv.math/0501191,
title = {Mad Subalgebras of Rings of Differential Operators on Curves},
author = {Yuri Berest and George Wilson},
journal= {arXiv preprint arXiv:math/0501191},
year = {2007}
}
Comments
Revised (and slightly extended) version, 25 pages; to appear in Advances in Math. (2007)