Note on Three-Dimensional Lie Groups
Glasgow mathematical journal, Tome 2 (1955) no. 3, pp. 112-115
Voir la notice de l'article provenant de la source Cambridge University Press
The object of this note is to construct a set of real three-dimensional Lie groups such that every real three-dimensional Lie group is locally isomorphic with some group in the set. The construction is effected by first finding canonical forms for the constants of structure of real three-dimensional Lie algebras; these canonical forms give rise to certain bilinear forms, and the Lie groups are obtained as linear groups isomorphic with groups of automorphisms which leave these bilinear forms invariant.
Patterson, E. M. Note on Three-Dimensional Lie Groups. Glasgow mathematical journal, Tome 2 (1955) no. 3, pp. 112-115. doi: 10.1017/S2040618500033153
@article{10_1017_S2040618500033153,
author = {Patterson, E. M.},
title = {Note on {Three-Dimensional} {Lie} {Groups}},
journal = {Glasgow mathematical journal},
pages = {112--115},
year = {1955},
volume = {2},
number = {3},
doi = {10.1017/S2040618500033153},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500033153/}
}
[†] † See, for example, C. Chevalley, “Theory of Lie groups” (princeton University press), Chapter IV.
[‡] ‡ The suffixes i, j, k, p, q take the values 1, 2, 3 and the summation convention for repeated indices is used.
[§] § Chevalley, loc. cit.
[∥] ∥ |P| denotes the determinant of P, and P' denotes the transpose of P.
Cité par Sources :