Invariant Differential Operators
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Vladimir K. Dobrev
Topics
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
With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups.
Contents
Quantum Groups and Quantum Algebras
Highest-Weight Modules over Quantum Algebras
Positive-Energy Representations of Noncompact Quantum Algebras
Duality for Quantum Groups
Invariant q-Difference Operators
Invariant q-Difference Operators Related to GLq(n)
q-Maxwell Equations Hierarchies
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
With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras.
This fourth volume covers AdS/CFT, Virasoro and affine (super-)algebras.
