• ystael@beehaw.org
      link
      fedilink
      English
      arrow-up
      6
      ·
      9 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
        link
        fedilink
        English
        arrow-up
        4
        ·
        9 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 :)

  • LordGimp@lemm.ee
    link
    fedilink
    English
    arrow-up
    2
    arrow-down
    2
    ·
    edit-2
    9 days ago

    That’s the sound I make when I see boobies.

    Hooga aei