TY  - GEN
N2  - 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.
DO  - 10.1007/978-3-030-52
AB  - 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.
T1  - Complex Semisimple Quantum Groups and Representation Theory /
ET  - 1st ed. 2020.
VL  - 2264
ID  - 944019
KW  - Group theory.
KW  - Functional analysis.
KW  - Topological groups.
KW  - Lie groups.
KW  - Associative rings.
KW  - Rings (Algebra)
KW  - Harmonic analysis.
SN  - 9783030524630
SN  - 3030524639
TI  - Complex Semisimple Quantum Groups and Representation Theory /
LK  - https://univsouthin.idm.oclc.org/login?url=https://dx.doi.org/10.1007/978-3-030-52463-0
UR  - https://univsouthin.idm.oclc.org/login?url=https://dx.doi.org/10.1007/978-3-030-52463-0
ER  -