Quantum Groups and Their Primitive Ideals

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The book delves into advanced concepts of quantum groups, focusing on the construction of Rq[G] through a general quadratic algebra and its requirements as a comodule. It emphasizes the tensor structure of the category of modules, necessitating a braided structure and the existence of an R-matrix that adheres to the quantum Yang-Baxter equation. The search for a self-dual model for Rq[G] leads to insights by V. G. Drinfeld, particularly concerning the Borel part of Uq(g) and the Drinfeld double, revealing a deep interconnection among various approaches in the context of semisimple groups.