Quantized semisimple Lie groups

These notes present a quick introduction to the q-deformations of semisimple Lie groups from the point of view of unitary representation theory. In order to remain concrete, we concentrate entirely on the case of the lie algebra sl(2,ℂ) and its associated compact and complex semisimple Lie groups SU(2) and SL(2,ℂ). We treat the following topics: The quantized enveloping algebra and its representations; Hopf algebras and the various notions of quantum groups; real structures; quantized algebras of functions on a compact semisimple group; quantized convolution algebras; the Peter-Weyl theorem; quantized complex semisimple Lie groups as quantum doubles; representations of quantized complex semisimple Lie groups; the quantum analogue of Harish-Chandra's Plancherel formula.