02491nam 2200469 450 991048373320332120221219232732.03-030-52463-910.1007/978-3-030-52463-0(OCoLC)1237305709(CKB)4100000011469458(MiAaPQ)EBC6357268(DE-He213)978-3-030-52463-0(PPN)250220466(EXLCZ)99410000001146945820210225d2020 uy 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierComplex semisimple quantum groups and representation theory /Christian Voigt, Robert Yuncken1st ed. 2020.Cham, Switzerland :Springer,[2020]©20201 online resource (X, 376 p. 25 illus.)Lecture Notes in Mathematics,0075-8434 ;22643-030-52462-0 This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.Lecture Notes in Mathematics,0075-8434 ;2264Group theoryGroup theory.512.2Voigt Christian791281Yuncken RobertMiAaPQMiAaPQMiAaPQBOOK9910483733203321Complex semisimple quantum groups and representation theory2351482UNINA