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

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

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

Geometric Topology 2024-01-17 v2 Quantum Algebra Representation Theory

Authors: 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.

Keywords

witt algebra foams gl_n-webs sl_2-action positive characteristic p-dg structure

Cite

@article{arxiv.2212.10106,
  title  = {Symmetries of $\mathfrak{gl}_N$-foams},
  author = {You Qi and Louis-Hadrien Robert and Joshua Sussan and Emmanuel Wagner},
  journal= {arXiv preprint arXiv:2212.10106},
  year   = {2024}
}

Comments

v1: 34 pages, many figures. Comments welcome! v2: 35 pages, exposition improved following referee's comments

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

Abstract

Keywords

Cite

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