matrix Lie algebra
Formal Lie groupoids
A matrix Lie algebra is the Lie algebra that is canonically a sub-Lie algebra of the general linear algebra? of matrices.
See also matrix Lie group.
By Ado’s theorem, every finite-dimensional Lie algebra over a field of characteristic zero is a matrix Lie algebra. A similar statement fails for Lie groups. Ado’s theorem has been used as a major step in the traditional proofs of the Cartan–Lie theorem on the existence of integration of Lie algebras to Lie groups.
Revised on September 22, 2010 04:21:06
by Toby Bartels