Frontmatter -- Preface -- Contents -- 1 Quantum Groups and Quantum Algebras -- 2 Highest-Weight Modules over Quantum Algebras -- 3 Positive-Energy Representations of Noncompact Quantum Algebras -- 4 Duality for Quantum Groups -- 5 Invariant q-Difference Operators -- 6 Invariant q-Difference Operators Related to GLq(n) -- 7 q-Maxwell Equations Hierarchies -- Bibliography -- Author Index -- Subject Index

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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

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In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)