Non-degeneracy of Hopf triplets

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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.36632
Primary Topic
Advanced Topics in Algebra
Type
preprint
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preprint

Non-degeneracy of Hopf triplets

Tomoro Mochida
arXiv (Cornell University)
Advanced Topics in Algebra
preprint

Non-degeneracy of Hopf triplets

Tomoro Mochida
preprint en

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.

arXiv (Cornell University)
Advanced Topics in Algebra
DOIOpen Access PDFOpenAlex
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Non-degeneracy of Hopf triplets — Tomoro Mochida · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS