Extensions and Well's type exact sequence of skew braces
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866914954914824192 |
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| author | Nishant |
| author_facet | Nishant |
| contents | In this article, we give a description of the split exact sequences of left skew braces. We define a free action of the second cohomology group of a left skew brace $H$ by $Ann(I)$ on $Ext_α(H, I)$ and show that this action becomes transitive if $I$ is a trivial skew brace. We also generalize the Well's type exact sequence for extensions by the trivial skew brace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_10343 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Extensions and Well's type exact sequence of skew braces Nishant Group Theory 20E22, 20J05, 20J06, 16T25 In this article, we give a description of the split exact sequences of left skew braces. We define a free action of the second cohomology group of a left skew brace $H$ by $Ann(I)$ on $Ext_α(H, I)$ and show that this action becomes transitive if $I$ is a trivial skew brace. We also generalize the Well's type exact sequence for extensions by the trivial skew brace. |
| title | Extensions and Well's type exact sequence of skew braces |
| topic | Group Theory 20E22, 20J05, 20J06, 16T25 |
| url | https://arxiv.org/abs/2112.10343 |