Introduction to Quantum Groups

DOI10.1007/978-3-031-23817-8arXiv1909.08152OpenAlexW4283701810MaRDI QIDQ6046397

Teodor Banica

Publication date: 11 May 2023

Abstract: This is an introduction to the quantum groups, or rather to the simplest quantum groups. The idea is that the unitary group $U_N$ has a free analogue $U_N^{+}$, whose standard coordinates $u_{ij}inC(U_N^{+})$ are allowed to be free, and the closed subgroups $Gsubset{U}_N^{+}$ can be thought of as being the compact quantum Lie groups. There are many interesting examples of such quantum groups, for the most designed in order to help with questions in quantum mechanics and statistical mechanics, and some general theory available as well, including Peter-Weyl theory, Tannakian duality, Brauer theorems and Weingarten integration. We discuss here the basic aspects of all this.

Full work available at URL: https://arxiv.org/abs/1909.08152

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

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