Algebra publication
Title
Invariants under tori of rings of differential operators
and related topics.
Author(s)
I.M. Musson,
M. Van den Bergh.
Year
1995
Abstract
If $G$ is a reductive algebraic group acting rationally
on a smooth affine variety $X$
then it
is generally believed that $D(X)^G$ has properties very similar to
those of enveloping algebras of semisimple Lie algebras. In this paper we
show that this is indeed the case when $G$ is a torus and $X=k^r\times
(k^*)^s$. We give a precise description of the primitive ideals in
$D(X)^G$ and we study in detail the ring theoretical and
homological properties of the minimal primitive quotients of $D(X)^G$. The
latter are of the form $D(X)^G/(\g-\chi(\g))$ where $\g=\Lie(G)$,
$\chi\in \g^\ast$ and $\g-\chi(\g)$ is the set of all $v-\chi(v)$ with
$v\in \g$. They occur as rings of twisted differential
operators on toric varieties.
As a side result we prove that if $G$ is a torus acting
rationally on a smooth affine variety then $D(X\quot G)$ is a simple ring.
DVI-file
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PS-file
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