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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 14th 2016
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexWith that account of PDEs as coalgebras of the jet comonad we saw described here, is there any insight to be shone on what's being discussed [here](https://golem.ph.utexas.edu/category/2016/05/e8_as_the_symmetries_of_a_pde.html): >Let’s begin with that model of $\mathrm{G}_2$ due to Cartan: the Lie algebra $\mathfrak{g}_2$ is formed by the infinitesimal symmetries of the system of PDE $u_{xx} = \frac{1}{3} (u_{yy})^3, \quad u_{xy} = \frac{1}{2} (u_{yy})^2$?

   With that account of PDEs as coalgebras of the jet comonad we saw described here, is there any insight to be shone on what’s being discussed here:

   Let’s begin with that model of $\mathrm{G}_2$ due to Cartan: the Lie algebra $\mathfrak{g}_2$ is formed by the infinitesimal symmetries of the system of PDE $u_{xx} = \frac{1}{3} (u_{yy})^3, \quad u_{xy} = \frac{1}{2} (u_{yy})^2$?