Invariants Under Tori of Rings of Differential Operators and Related Topics is popular PDF and ePub book, written by Ian Malcolm Musson in 1998, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Invariants Under Tori of Rings of Differential Operators and Related Topics can be Read Online from any device for your convenience.
Invariants Under Tori of Rings of Differential Operators and Related Topics Book PDF Summary
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.
Detail Book of Invariants Under Tori of Rings of Differential Operators and Related Topics PDF
- Author : Ian Malcolm Musson
- Release : 28 June 1998
- Publisher : American Mathematical Soc.
- ISBN : 9780821808856
- Genre : Mathematics
- Total Page : 100 pages
- Language : English
- PDF File Size : 18,7 Mb
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