Free commutative skew braces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918069227487232 |
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| author | Letourmy, Thomas |
| author_facet | Letourmy, Thomas |
| contents | 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 $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free commutative skew braces Letourmy, Thomas Group Theory Commutative Algebra Rings and Algebras 08B20, 16T25, 08A30 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 $X$. |
| title | Free commutative skew braces |
| topic | Group Theory Commutative Algebra Rings and Algebras 08B20, 16T25, 08A30 |
| url | https://arxiv.org/abs/2506.19765 |