## University of Sydney Algebra Seminar

# Karen Dancer (University of Queensland)

## Friday 20th November, 12.05-12.55pm, Carslaw 375

### Hopf algebras and solutions to the Yang-Baxter equation

A Hopf algebra is a structure that is simultaneously an algebra and a co-algebra. In the 1980's V.G. Drinfeld developed a double construction, which embeds any Hopf algebra in a larger Hopf algebra that is inherently quasi-triangular. A consequence of this is that the double algebra provides a solution to the Yang-Baxter equation. In this talk I will introduce Hopf algebras and outline the Drinfeld double construction, focusing on the example of finite group algebras. I will briefly discuss their representation theory before using them to construct solutions to the Yang-Baxter equation, which in turn lead to integrable models with finite group symmetry.