Cartan subalgebra
Let be a Lie algebra. Then a Cartan subalgebra
is a maximal subalgebra
of which is self-normalizing, that is, if for all , then as well. Any Cartan subalgebra is nilpotent
, and if is semi-simple
, it is abelian
. All Cartan subalgebras of a Lie algebra are conjugate by the adjoint action of any Lie group with algebra .
The dimension of is called the rank of .
Title | Cartan subalgebra |
---|---|
Canonical name | CartanSubalgebra |
Date of creation | 2013-03-22 13:20:09 |
Last modified on | 2013-03-22 13:20:09 |
Owner | bwebste (988) |
Last modified by | bwebste (988) |
Numerical id | 7 |
Author | bwebste (988) |
Entry type | Definition |
Classification | msc 17B20 |
Defines | rank of a Lie algebra |