The equation shown is a type of decomposition of a Lie algebra g that was introduced by Élie Cartan in his doctoral thesis. h is called a Cartan subalgebra of g.
To answer what a Lie algebra is, an extremely hand-wavy description might be: a Lie group is a continuous group of symmetries of some geometric object (for example, the group SO(3) of rotations of three-dimensional space), and the corresponding Lie algebra is the “tangent space” to the group, that is, the space of tiny changes you can make that lie “along” the group.
A lot of things in Lie theory and differential geometry are named after Élie Cartan, or sometimes after his son Henri.
Stupid person here, anyone mind explaining the joke?
It’s more of a math meme: Cartan Subalgebra.
I see gothic small letters my brain goes LIE!
lmao I went down a whole rabbit hole with the links in this page and I do not understand ANYTHING here. math is not my thing
The equation shown is a type of decomposition of a Lie algebra g that was introduced by Élie Cartan in his doctoral thesis. h is called a Cartan subalgebra of g.
To answer what a Lie algebra is, an extremely hand-wavy description might be: a Lie group is a continuous group of symmetries of some geometric object (for example, the group SO(3) of rotations of three-dimensional space), and the corresponding Lie algebra is the “tangent space” to the group, that is, the space of tiny changes you can make that lie “along” the group.
A lot of things in Lie theory and differential geometry are named after Élie Cartan, or sometimes after his son Henri.
I thought I was getting the idea until your example. Now I’m just going to nod and say thank you for explaining enough that I get the joke :)