Symmetries of $\mathfrak{gl}_N$-foams

TL;DR

This paper introduces a Lie algebra action on $rak{gl}_N$-foams that preserves evaluation formulas and induces an $rak{sl}_2$-action on web state spaces, enabling p-DG structures in positive characteristic.

Contribution

It establishes a Lie subalgebra action on foams compatible with evaluation formulas, leading to new algebraic structures on web state spaces.

Findings

Defined a Lie subalgebra action on foams

Established compatibility with $rak{gl}_N$-foam evaluation

Enabled p-DG structures in positive characteristic

Abstract

We give an action of a Lie subalgebra of the Witt algebra on foams. This action is compatible with the $\mathfrak{gl}_N$-foam evaluation formula. In particular, this endows states spaces associated with $\mathfrak{gl}_N$-webs with an $\mathfrak{sl}_2$-action. When working in positive characteristic, this can be used to define a $p$-DG structure on these state spaces.