2026-05-29T23:32:06Zhttps://riuma.uma.es/rest/oai/requestoai:riuma.uma.es:10630/282572026-02-03T12:11:15Zcom_10630_2254col_10630_37959
RIUMA. Repositorio Institucional de la Universidad de Málaga
author
Draper-Fontanals, Cristina
2023-12-12T12:10:07Z
2023-12-12T12:10:07Z
2023
https://hdl.handle.net/10630/28257
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.
eng
Lie, Algebras de, excepcionales
The Exceptional Lie algebra G_2.
conference output
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URL
https://riuma.uma.es/bitstreams/b6326940-c67f-46e9-b7df-c2ad8fac559f/download
File
MD5
fab54fc852fa19ef2cb6746a91c1b819
6249244
application/pdf
apoyo_visualCIMPA_Vitoria23.pdf