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Skein theory and deformations
Abstract
We use skein theoretic `recognition' theorems to classify deformations of certain pivotal or ribbon monoidal categories. We first show that a slight generalization of Kuperberg's characterization of quantum G2 shows that any infinitesimal deformation of quantum G2 as a pivotal category arises by varying q. This result applies both at generic q, and for the category of tilting modules at q a root of unity (provided we exclude a few small roots of unity). Second, we prove a new Kuperberg-like characterization of Deligne's St and use it to show that any infinitesimal deformation of St (excluding t=0) as a ribbon category comes from varying t.
Related
BibTeX
@misc{snyder2026skein,
title = {{Skein theory and deformations}},
author = {Noah Snyder and Benjamin Spencer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19329},
eprint = {2609.19329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19329},
}
RIS
TY - UNPB
TI - Skein theory and deformations
AU - Noah Snyder
AU - Benjamin Spencer
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19329
UR - https://arxiv.org/abs/2609.19329
AB - We use skein theoretic `recognition' theorems to classify deformations of certain pivotal or ribbon monoidal categories. We first show that a slight generalization of Kuperberg's characterization of quantum G_2 shows that any infinitesimal deformation of quantum G_2 as a pivotal category arises by varying q. This result applies both at generic q, and for the category of tilting modules at q a root of unity (provided we exclude a few small roots of unity). Second, we prove a new Kuperberg-like characterization of Deligne's S_t and use it to show that any infinitesimal deformation of S_t (excluding t=0) as a ribbon category comes from varying t.
ER -