Comment on Anyone up for a game of Cartan?

AFallingAnvil@lemmy.ca ⁨3⁩ ⁨weeks⁩ ago

• Phoenix3875@lemmy.world ⁨3⁩ ⁨weeks⁩ ago

  It’s more of a math meme: Cartan Subalgebra.

  source

  • Cattypat@lemmy.blahaj.zone ⁨3⁩ ⁨weeks⁩ ago

    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

    source
  • iAvicenna@lemmy.world ⁨3⁩ ⁨weeks⁩ ago

    I see gothic small letters my brain goes LIE!

    source
• ystael@beehaw.org ⁨3⁩ ⁨weeks⁩ 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.

  source

  • AFallingAnvil@lemmy.ca ⁨2⁩ ⁨weeks⁩ 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 :)

    source