PreprintCC BY 4.0arXiv
On the Mext groups of sVec_R and sVec_H
Abstract
We compute the groups of minimal nondegenerate extensions of the real symmetric fusion categories sVecℝ and sVecℍ. We find that they are both isomorphic to the Klein-four group (ℤ/2ℤ)2. Along the way, we classify all nondegenerately braided fusion categories over ℝ that have Frobenius-Perron dimension 4, and we determine exactly which of these categories is a Drinfeld center. We end the paper by discussing a homotopy-theoretic conjecture that organizes all these structures.
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BibTeX
@misc{sanford2026mext,
title = {{On the Mext groups of sVec_R and sVec_H}},
author = {Sean Sanford},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.20153},
eprint = {2609.20153},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20153},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Mext groups of sVec_R and sVec_H
AU - Sean Sanford
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.20153
UR - https://arxiv.org/abs/2609.20153
AB - We compute the groups of minimal nondegenerate extensions of the real symmetric fusion categories sVec_ℝ and sVec_ℍ. We find that they are both isomorphic to the Klein-four group (ℤ/2ℤ)^2. Along the way, we classify all nondegenerately braided fusion categories over ℝ that have Frobenius-Perron dimension 4, and we determine exactly which of these categories is a Drinfeld center. We end the paper by discussing a homotopy-theoretic conjecture that organizes all these structures.
ER -