2026-05-30T16:22:31Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/136092026-02-03T11:47:58Zcom_10630_2254col_10630_37959

G2 and the rolling ball Huerta, John Lie, Álgebras de, excepcionales Understanding the exceptional Lie groups as the symmetry groups of simpler objects is a long-standing program in mathematics. Here, we explore one famous realization of the smallest exceptional Lie group, G2: Its Lie algebra g2 acts locally as the symmetries of a ball rolling on a larger ball, but only when the ratio of radii is 1:3. Using the split octonions, we devise a similar, but more global, picture of G2: it acts as the symmetries of a `spinorial ball rolling on a projective plane', again when the ratio of radii is 1:3. We describe the incidence geometry of both systems, and use it to explain the mysterious 1:3 ratio in simple, geometric terms. 2017-05-09T12:29:44Z 2017-05-09T12:29:44Z 2017 2017-05-09 conference output http://hdl.handle.net/10630/13609 spa G2 and the rolling ball Málaga, España 11, May, 2017 open access by-nc-nd