**SMS scnews item created by James East at Tue 17 Nov 2009 1634**

Type: Seminar

Modified: Tue 17 Nov 2009 1641

Distribution: World

Expiry: 20 Nov 2009

**Calendar1: 20 Nov 2009 1205-1255**

**CalLoc1: Carslaw 375**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

# Hopf algebras and solutions to the Yang-Baxter equation

### Karen Dancer

#### Friday November 20, 12:05--12:55pm, Carslaw 375

###### Abstract

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.

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After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East jamese@maths.usyd.edu.au