Invariants under Tori of Rings of Differential Operators and Related Topics - Brossura

Musson, Ian M.; Van Den Bergh, Michel

Brossura

ISBN 10: 0821808850 ISBN 13: 9780821808856

Casa editrice: American Mathematical Society, 1998

Riassunto

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.

Dettagli dell'edizione

• Editore: American Mathematical Society
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0821808850
• ISBN 13: 9780821808856
• Rilegatura: Copertina flessibile
• Numero di pagine: 85
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile