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Quantized semisimple Lie groups

Rita FioresiRobert Yuncken — 2024

Archivum Mathematicum

The goal of this expository paper is to give a quick introduction to q -deformations of semisimple Lie groups. We discuss principally the rank one examples of 𝒰 q ( 𝔰𝔩 2 ) , 𝒪 ( SU q ( 2 ) ) , 𝒟 ( SL q ( 2 , ) ) and related algebras. We treat quantized enveloping algebras, representations of 𝒰 q ( 𝔰𝔩 2 ) , generalities on Hopf algebras and quantum groups, * -structures, quantized algebras of functions on q -deformed compact semisimple groups, the Peter-Weyl theorem, * -Hopf algebras associated to complex semisimple Lie groups and the Drinfeld double, representations...

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