Invariants under tori of rings of differential operators and related topics Ian M. Musson, Michel Van den Bergh. Memoirs of the American Mathematical Society 650.

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

ISBN 10: 0821808850 / ISBN 13: 9780821808856

Published by Providence, American Mathematical Society, 1998

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 16 MUS 9780821808856 Sprache: Englisch Gewicht in Gramm: 550.

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Bibliographic Details

• Title: Invariants under tori of rings of differential operators and related topics Ian M. Musson, Michel Van den Bergh. Memoirs of the American Mathematical Society 650.
• Publisher: Providence, American Mathematical Society
• 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.