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arXiv · 2506.19765

Free commutative skew braces

Thomas Letourmy
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Abstract

The main result of this paper is an explicit construction of the free commutative skew brace -- that is, a skew brace whose circle group is commutative -- on an arbitrary generating set $X$. We embed this object into a set of rational functions and show that a simple linear equation characterizes the image of this embedding. As a consequence, comparing elements in this skew brace is no more difficult than comparing elements in the free commutative group generated by $X$.

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Thomas Letourmy. 2025-06-24. Free commutative skew braces. https://arxiv.org/abs/2506.19765

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