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Differential invariants --- Invariants, Differential --- Continuous groups --- Differential invariants. --- Differential operators. --- Lie algebras. --- Lie groups. --- Geometry, Differential. --- Géométrie différentielle. --- Invariants différentiels. --- Géométrie différentielle. --- Invariants différentiels.

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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. ContentsQuantum Groups and Quantum AlgebrasHighest-Weight Modules over Quantum AlgebrasPositive-Energy Representations of Noncompact Quantum AlgebrasDuality for Quantum GroupsInvariant q-Difference OperatorsInvariant q-Difference Operators Related to GLq(n)q-Maxwell Equations Hierarchies

Quantum groups. --- Differential invariants. --- Differential operators. --- Operators, Differential --- Differential equations --- Operator theory --- Invariants, Differential --- Continuous groups --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory

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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

Lie algebras. --- Lie groups. --- Differential invariants. --- Differential operators. --- Quantum groups. --- Superalgebras. --- Nonassociative algebras --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory --- Operators, Differential --- Differential equations --- Operator theory --- Invariants, Differential --- Continuous groups --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups