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Item Details
| Title:
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INVARIANTS UNDER TORI OF RINGS OF DIFFERENTIAL OPERATORS AND RELATED TOPICS
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| By: |
Ian M. Musson, Michel van den Bergh |
| Format: |
Paperback |
| List price:
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£46.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821808850 |
| ISBN 13: |
9780821808856 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 January, 1998 |
| Series: |
Memoirs of the American Mathematical Society No. 650 |
| Pages: |
85 |
| Description: |
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. This book shows that this is indeed the case when $G$ is a torus and $X=k^r\times (k^*)^s$. |
| 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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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