Gauss Annihilators and Chart Functoriality in Finite SL3 Lattice Gauge Algebras

Abstract

For a finite connected oriented graph C, let the vertex gauge group act on the affine SL3 link carrier, let D_C be its ring of differential operators, and let B_C be the invariant polynomial ring. We determine whether Ann_{D_C}(B_C) contains differential constraints beyond the left ideal generated by the infinitesimal Gauss operators. For every graph of cycle rank at least five, graph-theoretic codimension estimates prove that the gauge action is 2-large. The moment components form a regular sequence, and their zero shell is a prime normal complete intersection. A strict filtered Spencer resolution makes the associated graded Gauss quotient explicit, while a general invariant-theoretic annihilator theorem gives equality of the invariant annihilator and the Gauss left ideal. We then prove a lattice-specific functoriality theorem. Under an admissible enlargement of graph charts, both ideals contract exactly to their small-chart counterparts on the complete restriction normalizer, even though Gauss fields at boundary vertices do not generally embed by direct inclusion. These restriction maps compose on their natural domains and are equivariant under graph relabelling. The purpose is not to claim a new general annihilator theorem — Schwarz proved equality for every 1-large smooth affine action — but to verify those largeness hypotheses uniformly for graph gauge actions, make the singular-shell mechanism explicit in lattice variables, and establish compatibility with enlargement and restriction of charts. MSC 2020: Primary 81T13; Secondary 53D20, 14L30, 16S32.

Keywords

How to cite

Elliman, D. (2026). Gauss Annihilators and Chart Functoriality in Finite SL3 Lattice Gauge Algebras. Neuro-Symbolic Ltd technical report. https://doi.org/10.2139/ssrn.7372627

@techreport{elliman2026gaussannihilatorssl3,
  author      = {Elliman, David},
  title       = {Gauss Annihilators and Chart Functoriality in Finite SL3 Lattice Gauge Algebras},
  institution = {Neuro-Symbolic Ltd},
  year        = {2026},
  doi         = {10.2139/ssrn.7372627},
  url         = {https://neusym.ai/papers/gauss_annihilators_sl3/}
}