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Anyone up for a game of Cartan?
(mander.xyz)
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this post was submitted on 29 Nov 2024
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Science Memes
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Stupid person here, anyone mind explaining the joke?
It's more of a math meme: Cartan Subalgebra.
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
I see gothic small letters my brain goes LIE!
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 :)