Invariants under tori of rings of differential operators and related topics. Memoirs of the American Mathematical Society; 650.

Musson, Ian M.; Bergh, M. Van Den

ISBN 10: 0821808850 / ISBN 13: 9780821808856

Published by Providence, 1998

About this Item

Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-00815 9780821808856 Sprache: Englisch Gewicht in Gramm: 150.

Seller Inventory # 2484653

Bibliographic Details

• Title: Invariants under tori of rings of differential operators and related topics. Memoirs of the American Mathematical Society; 650.
• Publisher: Providence
• Publication Date: 1998
• Language: English
• ISBN 10: 0821808850
• ISBN 13: 9780821808856
• Binding: Softcover
• Seller catalogs:
  • SA MATHEMATIK

About this title

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 $D(X/\!/G)$ is a simple ring.