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G2 and the rolling ball
dc.contributor.author | Huerta, John | |
dc.date.accessioned | 2017-05-09T12:29:44Z | |
dc.date.available | 2017-05-09T12:29:44Z | |
dc.date.created | 2017 | |
dc.date.issued | 2017-05-09 | |
dc.identifier.uri | http://hdl.handle.net/10630/13609 | |
dc.description.abstract | 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. | es_ES |
dc.description.sponsorship | Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. | es_ES |
dc.language.iso | spa | es_ES |
dc.rights | info:eu-repo/semantics/openAccess | es_ES |
dc.subject | Lie, Álgebras de, excepcionales | es_ES |
dc.subject.other | Rolling balls | es_ES |
dc.subject.other | G2 | es_ES |
dc.title | G2 and the rolling ball | es_ES |
dc.type | info:eu-repo/semantics/conferenceObject | es_ES |
dc.centro | Facultad de Ciencias | es_ES |
dc.relation.eventtitle | G2 and the rolling ball | es_ES |
dc.relation.eventplace | Málaga, España | es_ES |
dc.relation.eventdate | 11, May, 2017 | es_ES |
dc.cclicense | by-nc-nd | es_ES |