LEADER 02489nam 2200469 450 001 996418259003316 005 20221219232732.0 010 $a3-030-52463-9 024 7 $a10.1007/978-3-030-52463-0 035 $a(OCoLC)1237305709 035 $a(CKB)4100000011469458 035 $a(MiAaPQ)EBC6357268 035 $a(DE-He213)978-3-030-52463-0 035 $a(PPN)250220466 035 $a(EXLCZ)994100000011469458 100 $a20210225d2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComplex semisimple quantum groups and representation theory /$fChristian Voigt, Robert Yuncken 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (X, 376 p. 25 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2264 311 $a3-030-52462-0 330 $aThis book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2264 606 $aGroup theory 615 0$aGroup theory. 676 $a512.2 700 $aVoigt$b Christian$0791281 702 $aYuncken$b Robert 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418259003316 996 $aComplex semisimple quantum groups and representation theory$92351482 997 $aUNISA