PreprintCC BY-NC-ND 4.0arXiv
Galois-modular obstructions to the categorification of near-group fusion rings
Abstract
In this article we establish new obstructions to the categorification of near-group fusion rings by combining the values of irreducible characters of the Grothendieck ring with the Galois symmetry of the induced unit object I(1) in the Drinfeld center. As a result, we show that a near-group ring of type G+m, where G is an abelian group and both |G| and m are odd, can only categorify if m=|G|.
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BibTeX
@misc{blasco2026galoismodular,
title = {{Galois-modular obstructions to the categorification of near-group fusion rings}},
author = {Víctor Blasco},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04232},
eprint = {2611.04232},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04232},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Galois-modular obstructions to the categorification of near-group fusion rings
AU - Víctor Blasco
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04232
UR - https://arxiv.org/abs/2611.04232
AB - In this article we establish new obstructions to the categorification of near-group fusion rings by combining the values of irreducible characters of the Grothendieck ring with the Galois symmetry of the induced unit object I(1) in the Drinfeld center. As a result, we show that a near-group ring of type G+m, where G is an abelian group and both |G| and m are odd, can only categorify if m=|G|.
ER -