∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
A matrix Lie algebra is the Lie algebra that is canonically a sub-Lie algebra of the general linear Lie 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.
Last revised on May 17, 2018 at 08:57:55. See the history of this page for a list of all contributions to it.