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

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arxiv 2212.10106 v2 pith:B6FR4QEC submitted 2022-12-20 math.GT math.QAmath.RT

You Qi , Louis-Hadrien Robert , Joshua Sussan , Emmanuel Wagner This is my paper · ORCID
classification math.GTmath.QAmath.RT
keywords mathfrakactionfoamsspacesalgebraassociatedcharacteristiccompatible
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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.

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  1. An action of the Witt algebra on Khovanov-Rozansky homology

    math.GT 2025-01 conditional novelty 6.0 of 10

    Khovanov-Rozansky gl_N link homology carries a functorial action of the positive Witt algebra, making link cobordisms equivariant maps between twisted homology groups.

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