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

You Qi, Louis-Hadrien Robert, Joshua Sussan, Emmanuel Wagner

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.

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

Abstract

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