Definition: Plateau and frozen gauge group

Choose a nonempty relatively compact open set $U$ with

Set ${\mathfrak{g}}_p={C_c}^{\infty }(U;T\hat{M})$. Its elements are extended by zero to the completion.

For $\xi ,\zeta \in {\mathfrak{g}}_p$, let $F_{\kappa }$ be the time-one flow of $\kappa \xi +{\kappa }^2\zeta$. The formal pullbacks

generate ${\mathcal{G}}_p$. This is the frozen plateau algebra; it is not the Killing algebra of the cone.