• ystael@beehaw.org
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      18 days ago

      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.

      • AFallingAnvil@lemmy.ca
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        18 days ago

        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 :)