Quantum Group and Quantum Symmetry

Details Quantum Group and Quantum Symmetry Quantum Group and Quantum Symmetry

1995-08-30

arxiv.org/abs/hep-th/9508170v1

Phys.Rept. 262 (1995) 137-225

Physics

High Energy Physics

High Energy Physics - Theory

127 pages, Latex

Scientific paper

This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for $q$ being a root of unity. Quantum symmetries are explored in selected topics of modern physics.

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