RT Conference Proceedings
T1 G2 and the rolling ball
A1 Huerta, John
K1 Lie, Álgebras de, excepcionales
AB Understanding the exceptional Lie groups as the symmetry groupsof simpler objects is a long-standing program in mathematics. Here, we exploreone famous realization of the smallest exceptional Lie group, G2: Its Lie algebrag2 acts locally as the symmetries of a ball rolling on a larger ball, but only whenthe ratio of radii is 1:3. Using the split octonions, we devise a similar, but moreglobal, picture of G2: it acts as the symmetries of a `spinorial ball rolling on aprojective plane', again when the ratio of radii is 1:3. We describe the incidencegeometry of both systems, and use it to explain the mysterious 1:3 ratio insimple, geometric terms.
YR 2017
FD 2017-05-09
LK http://hdl.handle.net/10630/13609
UL http://hdl.handle.net/10630/13609
LA spa
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026