PreprintCC BY 4.0arXiv
Action accessibility in the variety of skew braces
Abstract
In this paper, we answer negatively to a question posed in the context of the 2025 Oberwolfach Mini-Workshop ``The Yang-Baxter Equation and Representations of Braid Groups'' regarding the existence of split extensions classifiers in the category of skew braces. To this end, we show that the variety of skew braces is not action accessible by investigating the categorical notion of centraliser in the sense of Huq. In light of their intrinsic relationship with skew braces, an analogous result is proven for the variety of post-Lie algebras over a fixed field.
Versions
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BibTeX
@misc{albano2026action,
title = {{Action accessibility in the variety of skew braces}},
author = {Andrea Albano and Paola Stefanelli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.30097},
eprint = {2605.30097},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30097},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Action accessibility in the variety of skew braces
AU - Andrea Albano
AU - Paola Stefanelli
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2605.30097
UR - https://arxiv.org/abs/2605.30097
AB - In this paper, we answer negatively to a question posed in the context of the 2025 Oberwolfach Mini-Workshop ``The Yang-Baxter Equation and Representations of Braid Groups'' regarding the existence of split extensions classifiers in the category of skew braces. To this end, we show that the variety of skew braces is not action accessible by investigating the categorical notion of centraliser in the sense of Huq. In light of their intrinsic relationship with skew braces, an analogous result is proven for the variety of post-Lie algebras over a fixed field.
ER -