Cohomology of Linear Cycle Sets when the adjoint group is finite abelian
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908586752344064 |
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| author | Guccione, Jorge Guccione, Juan José Valqui, Christian |
| author_facet | Guccione, Jorge Guccione, Juan José Valqui, Christian |
| contents | This paper analyzes the second cohomology group of a linear cycle set with coefficients in an abelian group I, for linear cycle sets with commutative adjoint operation, focusing on the finite abelian case. It aims to classify extensions of such structures through cohomological methods. Techniques are developed to systematically construct explicitly 2-cocycles. Finally, some illustrative examples are explored to validate the theoretical framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology of Linear Cycle Sets when the adjoint group is finite abelian Guccione, Jorge Guccione, Juan José Valqui, Christian Group Theory This paper analyzes the second cohomology group of a linear cycle set with coefficients in an abelian group I, for linear cycle sets with commutative adjoint operation, focusing on the finite abelian case. It aims to classify extensions of such structures through cohomological methods. Techniques are developed to systematically construct explicitly 2-cocycles. Finally, some illustrative examples are explored to validate the theoretical framework. |
| title | Cohomology of Linear Cycle Sets when the adjoint group is finite abelian |
| topic | Group Theory |
| url | https://arxiv.org/abs/2506.12341 |