Invariants under Tori of Rings of Differential Operators and Related Topics (Memoirs of the AMS) - Softcover

Inhaltsangabe

If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X)$ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=kr\times (k*)s$. They give a precise description of the primitive ideals in $D(X)$ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X)$. The latter are of the form $Bx=D(X)/({\germ g}-\chi({\germ g}))$ where ${\germ g}= {\rm Lie}(G)$, $\chi\in {\germ g}ast$ and ${\germ g}-\chi({\germ g})$ is the set of all $v-\chi(v)$ with $v\in {\germ g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X/\!/G)$ is a simple ring.

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