RT Conference Proceedings
T1 The exceptional Lie group G2
A1 Draper-Fontanals, Cristina
K1 Lie, Algebras de, excepcionales
AB These notes have been prepared for the Workshop on "(Non)-existence ofcomplex structures on $\mathbb{S}^6$", to be celebrated in Marburg in March, 2017.The material is not intended to be original. It contains a survey about the smallest of the exceptional Lie groups: $G_2$, its definition and different characterizations joint with its relationship with $\mathbb{S}^6$. With the exception of the summary of the Killing-Cartan classification, this survey is self-contained, and all the proofs are given, mainly following linear algebra arguments. Although these proofs are well-known, they are spread and some of them are difficult to find. The approach is algebraical, working at the Lie algebra level most of times.  We analyze  the complex Lie algebra  (and group) of type $G_2$ as well as the two real Lie algebras of type $G_2$, the split and the compact one. Octonions will appear, but it is not the starting point. Also, 3-forms approach and spinorial approach are viewed and related.
YR 2017
FD 2017-04-05
LK http://hdl.handle.net/10630/13425
UL http://hdl.handle.net/10630/13425
LA eng
NO Lo que incluyo son las notas para pizarra de la propia conferencia.
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026