In this chapter, led by examples, we introduce the notions of Hopf algebra and quantum group. We study their geometry and in particular their Lie algebra (of left invariant vector fields). The examples of the quantum \(sl(2)\) Lie algebra and of the quantum (twisted) Poincaré Lie algebra \(iso_\theta(3,1)\) are presented.
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Aschieri, P. (2009). Quantum Groups, Quantum Lie Algebras, and Twists. In: Noncommutative Spacetimes. Lecture Notes in Physics, vol 774. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89793-4_7
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