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Non-degeneracy of Hopf triplets
Abstract
We study the relationship between semisimplicity and non-degeneracy for finite-dimensional Hopf triplets over a field of characteristic zero. The non-degeneracy condition appears in the construction of 4-manifold invariants from Hopf triplets, and it was not known whether non-semisimple examples satisfying this condition exist. We prove that a Hopf triplet is non-degenerate if and only if it is semisimple.
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BibTeX
@misc{mochida2026nondegeneracy,
title = {{Non-degeneracy of Hopf triplets}},
author = {Tomoro Mochida},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36632},
eprint = {2610.36632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36632},
}
RIS
TY - UNPB
TI - Non-degeneracy of Hopf triplets
AU - Tomoro Mochida
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36632
UR - https://arxiv.org/abs/2610.36632
AB - We study the relationship between semisimplicity and non-degeneracy for finite-dimensional Hopf triplets over a field of characteristic zero. The non-degeneracy condition appears in the construction of 4-manifold invariants from Hopf triplets, and it was not known whether non-semisimple examples satisfying this condition exist. We prove that a Hopf triplet is non-degenerate if and only if it is semisimple.
ER -