Invariants under Tori of Rings of Differential Operators and Related Topics (eBook)

Ian M Musson (Autor)

eBook Download: PDF

85 Seiten
American Mathematical Society (Verlag)
978-1-4704-0239-6 (ISBN)

Infos

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 ${/mathfrak g}= /mathrm{Lie}(G)$, $/chi/in {/mathfrak g}^/ast$ 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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 1-4704-0239-4 / 1470402394
• ISBN-13: 978-1-4704-0239-6 / 9781470402396