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book: Volume 1 Noncompact Semisimple Lie Algebras and Groups
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Volume 1 Noncompact Semisimple Lie Algebras and Groups

Part of the multi-volume work
Invariant Differential Operators
Language: English
Published/Copyright: 2016
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De Gruyter Studies in Mathematical Physics

About this book

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 / Editor information

Vladimir Dobrev, Bulgarian Academy of Sciences, Sofia, Bulgaria.

Reviews

"The book would be helpful for theoretical physicists interested in applications of representation theory."
Michael Pevzner in: Mathematical Reviews December 2017, MR3561099

Topics

  • Publicly Available

    Frontmatter

    I
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    Preface

    V
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    Contents

    VII
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    1. Introduction

    1
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    2. Lie Algebras and Groups

    11
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    3. Real Semisimple Lie Algebras

    93
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    4. Invariant Differential Operators

    133
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    5. Case of the Anti-de Sitter Group

    162
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    6. Conformal Case in 4D

    188
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    7. Kazhdan–Lusztig Polynomials, Subsingular Vectors, and Conditionally Invariant Equations

    238
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    8. Invariant Differential Operators for Noncompact Lie Algebras Parabolically Related to Conformal Lie Algebras

    271
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    9. Multilinear Invariant Differential Operators from New Generalized Verma Modules

    353
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    Bibliography

    375
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    Author Index

    403
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    Subject Index

    405
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    Backmatter

    409
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
September 12, 2016
eBook ISBN:
9783110427646
Hardcover published on:
September 12, 2016
Hardcover ISBN:
9783110435429
Pages and Images/Illustrations in book
Front matter:
12
Main content:
409
Tables:
9
https://doi.org/10.1515/9783110427646
eBook ISBN: 9783110427646
Hardcover ISBN: 9783110435429
Keywords for this book
Invarianter Differentialoperator; Superalgebra; Lie-Algebra; Quantengruppe
Audience(s) for this book
Researchers in Mathematics and Mathematical and Theoretical Physics.
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