RT Conference Proceedings
T1 The Exceptional Lie algebra G_2.
A1 Draper-Fontanals, Cristina
K1 Lie, Algebras de, excepcionales
AB The Killing-Cartan classification of finite-dimensional complex simple Lie algebras was one of the great milestones of 19th-century mathematics. According to it, there are four infinite families of classical simple Lie algebras (special linear, orthogonal, and symplectic) and five isolated "exceptional" examples, G_2, F_4, E_6, E_7 and E_8, of dimensions 14, 52, 78, 133 and 248 respectively. In this brief course, we would like to speak about the smallest of the exceptional algebras, G_2, as well as its relationship with another relevant nonassociative algebra, the octonion algebra, for which G_2 is the derivation algebra. We will use this example to illustrate the structure theory of simple Lie algebras over C, while giving some hints about the classification over the reals. Hopefully, we speak about the relevance of  G_2 to Geometry or Physics.
YR 2023
FD 2023
LK https://hdl.handle.net/10630/28257
UL https://hdl.handle.net/10630/28257
LA eng
NO Escuela de doctorado en países en vías de desarrollo: cursos de doctorado unidos a conferencias de investigación
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 28 feb 2026