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This ERGEBNISSE volume provides a comprehensive and detailed account of the research in the field of quantum groups. The book is a sequel to J. Dixmier: "Algebres enveloppantes", Gauthier-Villars 1974 and J.-C. Jantzen: "Einhüllende Algebren halbeinfacher Lie-Algebren", Springer-Verlag 1983. It is an important reference work for graduate students and researchers in algebra, the theory of Lie algebras, mathematical physics.
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