Mad Subalgebras of Rings of Differential Operators on Curves

Details Mad Subalgebras of Rings of Differential Operators on Curves Mad Subalgebras of Rings of Differential Operators on Curves

2005-01-12

arxiv.org/abs/math/0501191v3

Mathematics

Quantum Algebra

Revised (and slightly extended) version, 25 pages; to appear in Advances in Math. (2007)

Scientific paper

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.

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