Invariants Under Tori of Rings of Differential Operators and Related Topics (Memoirs of the AMS) - Couverture souple

Musson, Ian M.

Couverture souple

ISBN 10 : 0821808850 ISBN 13 : 9780821808856

Editeur : American Mathematical Society, 1999

Synopsis

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 book, the authors show that this is indeed the case when $G$ is a torus and $X=k^r\times (k^*)^s$. They give a precise description of the primitive ideals in $D(X)^G$ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X)^G$. The latter are of the form $B^x=D(X)^G/({\mathfrak g}-\chi({\mathfrak g}))$ where ${\mathfrak g}=\textnormal{Lie}(G)$, $\chi\in {\mathfrak g}^\ast$ and ${\mathfrak g}-\chi({\mathfrak g})$ is the set of all $v-\chi(v)$ with $v\in {\mathfrak g}$. 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 $D(X[LAMBDA]!/G)$ is a simple ring.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 1999
• Langue: anglais
• ISBN 10: 0821808850
• ISBN 13: 9780821808856
• Reliure: Broché
• Nombre de pages: 85
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible