# Split octonions and the rolling ball

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Ping Xu, Mathieu Stiénon, Nigel Higson.

**Speaker:** John Baez, UC Riverside

**Abstract:** Understanding exceptional Lie groups as the symmetry groups of more familiar objects is a fascinating challenge. The compact form of the smallest exceptional Lie group, G2, is the symmetry group of an 8-dimensional nonassociative algebra called the octonions. However, another form of this group arises as symmetries of a simple problem in classical mechanics! The space of configurations of a ball rolling on another ball without slipping or twisting defines a manifold where the tangent space of each point is equipped with a 2-dimensional subspace describing the allowed infinitesimal motions. Under certain special conditions, the split real form of G2 acts as symmetries. We can understand this using the quaternions together with an 8-dimensional algebra called the 'split octonions'. The rolling ball picture makes the geometry associated to G2 quite vivid. This is joint work with James Dolan and John Huerta.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 04/14/2015

**Time:** 2:30pm - 3:30pm