The University of Queensland
Department of Mathematics
Mathematical Physics Seminar
Quantum Algebras, Yang-Baxter Equation and Applications
Dr Y-Z Zhang
Department of Mathematics
The University of Queensland
Monday 31st July, 10.00am
67-316 Priestley Building
The notion of quantum algebras was introduced by Drinfeld (a Fields medalist) and Jimbo independently in 1985/86, following the initiatives of works by the St Petersberg group on the Yang-Baxter equation and integrable systems. Since their introduction, quantum algebras have been a high-profile research subject worldwide because of their ground-breaking applications in many branches of modern mathematics and physics such as knot theory and integrable models. The bridge in many such applications is the Yang-Baxter equation. Roughly speaking, quantum algebras are ``quantum" or $q$ deformations of simple Lie algebras. In this talk, I illustrate the idea by using as examples the Lie algebra $sl(2)$ and superalgebra $sl(1|1)$, leading to quantum algebra $U_q[sl(2)]$ and superalgebra $U_q[sl(1|1)]$. I also discuss applications of quantum algebras to knot theory and integrable models. Special attention is paid to the construction of solutions of the Yang-Baxter equation and the construction of integrable models from such solutions. In the last part of my talk, I outline the contributions I have made together with my colleagues on several fronts of the subject.
All interested are invited to attend.
Enquires to Yao-Zhong Zhang on 3365 2309 or yzz@maths.uq.edu.au