Extensions of a family of Linear Cycle Sets
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909456939352064 |
|---|---|
| author | Guccione, Jorge Guccione, Juan José Valqui, Christian |
| author_facet | Guccione, Jorge Guccione, Juan José Valqui, Christian |
| contents | This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and establish conditions under which the extensions are fully determined. Key results include a characterization of extensions when I lies in the socle of the extended structure and H is trivial, and the construction of explicit examples for both trivial and non-trivial cases. The paper provides a systematic approach to understanding the structure of these extensions, with applications to various families of abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions of a family of Linear Cycle Sets Guccione, Jorge Guccione, Juan José Valqui, Christian Group Theory K-Theory and Homology 55N35, 20E22, 16T25 This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and establish conditions under which the extensions are fully determined. Key results include a characterization of extensions when I lies in the socle of the extended structure and H is trivial, and the construction of explicit examples for both trivial and non-trivial cases. The paper provides a systematic approach to understanding the structure of these extensions, with applications to various families of abelian groups. |
| title | Extensions of a family of Linear Cycle Sets |
| topic | Group Theory K-Theory and Homology 55N35, 20E22, 16T25 |
| url | https://arxiv.org/abs/2501.08357 |