Zhe Chang — Page 8 | Searcharxiv

arXiv1999

Quantum Anti-de Sitter Space

The quantum Anti-de Sitter (AdS) group and quantum AdS space is discussed. Ways of getting the quantum AdS group from real forms of quantum orthogonal group are presented. Differential calculus on the quantum AdS space are also introduced. In particular, reality of differential calculus are given. We set up explicit relationships between quantum group and quantum algebra, which can be refereed as the quantum counterpart of the classical exponential. By this way, quantum AdS algebra is deduced from conjugation on the quantum AdS group.

hep-th↗

arXiv1995

Quantum Group and Quantum Symmetry

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.

hep-th↗