Invariant Differential Operators Noncompact Semisimple Lie Algebras And Groups PDF Download
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Author | : V. K. Dobrev |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : Differential invariants |
ISBN | : |
Download Invariant Differential Operators: Noncompact semisimple Lie algebras and groups Book in PDF, ePub and Kindle
"With applications in quantum field theory, elementary particle physics and general relativity, this four-volume work studies invariance of differential operators under Lie algebras, quantum groups, and superalgebras"--
Author | : Vladimir K. Dobrev |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 422 |
Release | : 2016-09-12 |
Genre | : Mathematics |
ISBN | : 3110427648 |
Download Noncompact Semisimple Lie Algebras and Groups Book in PDF, ePub and Kindle
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups. Contents: Introduction Lie Algebras and Groups Real Semisimple Lie Algebras Invariant Differential Operators Case of the Anti-de Sitter Group Conformal Case in 4D Kazhdan–Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant Equations Invariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie Algebras Multilinear Invariant Differential Operators from New Generalized Verma Modules Bibliography Author Index Subject Index
Author | : Vladimir K. Dobrev |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 511 |
Release | : 2016-09-12 |
Genre | : Mathematics |
ISBN | : 311042780X |
Download Noncompact Semisimple Lie Algebras and Groups Book in PDF, ePub and Kindle
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory supplemented by many concrete examples for a great variety of noncompact semisimple Lie algebras and groups. Contents: Introduction Lie Algebras and Groups Real Semisimple Lie Algebras Invariant Differential Operators Case of the Anti-de Sitter Group Conformal Case in 4D Kazhdan–Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant Equations Invariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie Algebras Multilinear Invariant Differential Operators from New Generalized Verma Modules Bibliography Author Index Subject Index
Author | : Franz W. Kamber |
Publisher | : American Mathematical Soc. |
Total Pages | : 131 |
Release | : 1971 |
Genre | : Differential operators |
ISBN | : 0821818139 |
Download Invariant Differential Operators and the Cohomology of Lie Algebra Sheaves Book in PDF, ePub and Kindle
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.
Author | : Alexander A. Kirillov |
Publisher | : Cambridge University Press |
Total Pages | : 237 |
Release | : 2008-07-31 |
Genre | : Mathematics |
ISBN | : 0521889693 |
Download An Introduction to Lie Groups and Lie Algebras Book in PDF, ePub and Kindle
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author | : Armand Borel |
Publisher | : American Mathematical Soc. |
Total Pages | : 184 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821802887 |
Download Essays in the History of Lie Groups and Algebraic Groups Book in PDF, ePub and Kindle
Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.
Author | : Mohsen Pazirandeh |
Publisher | : |
Total Pages | : 120 |
Release | : 1971 |
Genre | : Differential operators |
ISBN | : |
Download Some Results on Invariant Differential Operators on a Real Semi-simple Lie Algebra Book in PDF, ePub and Kindle
Author | : Vladimir K. Dobrev |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 246 |
Release | : 2019-04-01 |
Genre | : Mathematics |
ISBN | : 3110609711 |
Download AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras Book in PDF, ePub and Kindle
The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.
Author | : Vladimir K. Dobrev |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 226 |
Release | : 2018-09-24 |
Genre | : Mathematics |
ISBN | : 3110527499 |
Download Supersymmetry Book in PDF, ePub and Kindle
With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras
Author | : David Andrew Richter |
Publisher | : |
Total Pages | : 174 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Semisimple Lie Algebras of Differential Operators Book in PDF, ePub and Kindle