Invariants Under Tori Of Rings Of Differential Operators And Related Topics
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Invariants under Tori of Rings of Differential Operators and Related Topics
Author: Ian Malcolm Musson
language: en
Publisher: American Mathematical Soc.
Release Date: 1998
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=k \times (k ) $. 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 $B =D(X) /({\germ g}-\chi({\germ g}))$ 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.
Rings of Differential Operators on Classical Rings of Invariants
Author: Thierry Levasseur
language: en
Publisher: American Mathematical Soc.
Release Date: 1989
"September 1989, Volume 81, number 412 (third of 6 numbers)."
Inverse Invariant Theory and Steenrod Operations
Author: Mara D. Neusel
language: en
Publisher: American Mathematical Soc.
Release Date: 2000
This book is intended for researchers and graduate students in commutative algebra, algebraic topology and invariant theory.