Rings Of Differential Operators On Classical Rings Of Invariants

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Rings Of Differential Operators On Classical Rings Of Invariants

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Author : Thierry Levasseur
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Rings Of Differential Operators On Classical Rings Of Invariants written by Thierry Levasseur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

"September 1989, Volume 81, number 412 (third of 6 numbers)."

Rings Of Differential Operators

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Author : Jan-Erik Björk
language : en
Publisher: North-Holland
Release Date : 1979

Rings Of Differential Operators written by Jan-Erik Björk and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.

Differential Operators On Invariant Rings Of Tori And Related Topics

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Author : Sonia L. Rueda
language : en
Publisher:
Release Date : 2002

Differential Operators On Invariant Rings Of Tori And Related Topics written by Sonia L. Rueda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Differential operators categories.

Invariants Under Tori Of Rings Of Differential Operators And Related Topics

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Author : Ian Malcolm Musson
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Invariants Under Tori Of Rings Of Differential Operators And Related Topics written by Ian Malcolm Musson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X) $ 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 \times (k ) $. They give a precise description of the primitive ideals in $D(X) $ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X) $. The latter are of the form $B =D(X) /({\germ g}-\chi({\germ g}))$ where ${\germ g}= {\rm Lie}(G)$, $\chi\in {\germ g} ast$ and ${\germ g}-\chi({\germ g})$ is the set of all $v-\chi(v)$ with $v\in {\germ g}$. 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.

Invariants Under Tori Of Rings Of Differential Operators And Related Topics

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Author : Ian Malcolm Musson
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11

Invariants Under Tori Of Rings Of Differential Operators And Related Topics written by Ian Malcolm Musson and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with MATHEMATICS categories.

If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X) $ 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 \times (k ) $. They give a precise description of the primitive ideals in $D(X) $ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X) $. The latter are of the form $B =D(X) /({\germ g}-\chi({\germ g}))$ where ${\germ g}= {\rm Lie}(G)$, $\chi\in {\germ g} ast$ and ${\germ g}-\chi({\germ g})$ is the set of all $v-\chi(v)$ with $v\in {\germ g}$. 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.

Invariant Differential Operators For Quantum Symmetric Spaces

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Author : Gail Letzter
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Invariant Differential Operators For Quantum Symmetric Spaces written by Gail Letzter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.

Commutative Algebra And Its Interactions To Algebraic Geometry

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Author : Nguyen Tu CUONG
language : en
Publisher: Springer
Release Date : 2018-08-02

Commutative Algebra And Its Interactions To Algebraic Geometry written by Nguyen Tu CUONG and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Mathematics categories.

This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.

On The Center Of The Ring Of Invariant Differential Operators On Semisimple Groups Over Fields Of Positive Characteristic

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Author : Hongfei Tian
language : en
Publisher:
Release Date : 2017

On The Center Of The Ring Of Invariant Differential Operators On Semisimple Groups Over Fields Of Positive Characteristic written by Hongfei Tian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

Invariant Differential Operators And The Cohomology Of Lie Algebra Sheaves

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Author : Franz W. Kamber
language : en
Publisher: American Mathematical Soc.
Release Date : 1971

Invariant Differential Operators And The Cohomology Of Lie Algebra Sheaves written by Franz W. Kamber and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Differential operators categories.

For a Lie algebra sheaf L of derivations of a sheaf of rings O on a space X global cohomology groups and local cohomology sheaves are introduced and analyzed. Global and local splitting obstructions for extensions of modules over a Lie algebra sheaf are studied. In the applications considered, L is a Lie algebra sheaf of vector fields on a manifold M, O the structure sheaf of M. For vector bundles E, F on M on which L acts, the existence of invariant differential operators D: E→F whose symbols are preassigned equivariant maps is discussed in terms of these splitting obstructions. Lie algebra sheaves defined by Lie group actions are considered. This theory is applied in particular to the case of a transitive L. The splitting obstructions for extensions of modules over a transitive Lie algebra sheaf are analyzed in detail. The results are then applied to the problem of the existence of invariant connections on locally homogeneous spaces. The obstruction is computed in some examples.

Unit Groups Of Classical Rings

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Author : Gregory Karpilovsky
language : en
Publisher:
Release Date : 1988

Unit Groups Of Classical Rings written by Gregory Karpilovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

The purpose of this book is to give a self-contained, up-to-date account of the structure of unit groups of classical rings. In so doing, the work draws together four areas of mathematics: ring theory, group theory, group representation theory, and algebraic number theory. The ensuing interplay between these disciplines provides a unique source of enrichment for each of them. The main theme centers on two related problems: to determine the isomorphism class of the unit group (U)R of ring R in terms of natural invariants associated with R; and to find an effective method for the construction of units of ring R. Various threads of the development are tied together to convey a comprehensive picture of the current state of the subject. Examples are provided to help research workers who need to compute explicitly unit groups of certain rings. A familiarity with basic ring-theoretic and group-theoretic concepts is assumed, but a chapter on algebraic preliminaries is included. The text is distinguished by its very clear exposition.