Hochschild cohomology groups of 5-dimensional complex nilpotent associative algebras
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914191418327040 |
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| author | Mosbahi, Bouzid Basdouri, Imed Lerbet, Jean |
| author_facet | Mosbahi, Bouzid Basdouri, Imed Lerbet, Jean |
| contents | This paper explores the structure of low-dimensional cohomology groups in the context of complex nilpotent associative algebras. Specifically, we study 5-dimensional complex nilpotent associative algebras satisfying $\mathcal{A}^4 = 0$ and $\mathcal{A}^3 \neq 0$. Using their isomorphism invariants, we compute and present the zeroth and first Hochschild cohomology groups, $H^0(\mathcal{A}, \mathcal{A})$ and $H^1(\mathcal{A}, \mathcal{A})$, in explicit matrix form. These results show how cohomology helps to identify and classify different associative algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09346 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hochschild cohomology groups of 5-dimensional complex nilpotent associative algebras Mosbahi, Bouzid Basdouri, Imed Lerbet, Jean Rings and Algebras This paper explores the structure of low-dimensional cohomology groups in the context of complex nilpotent associative algebras. Specifically, we study 5-dimensional complex nilpotent associative algebras satisfying $\mathcal{A}^4 = 0$ and $\mathcal{A}^3 \neq 0$. Using their isomorphism invariants, we compute and present the zeroth and first Hochschild cohomology groups, $H^0(\mathcal{A}, \mathcal{A})$ and $H^1(\mathcal{A}, \mathcal{A})$, in explicit matrix form. These results show how cohomology helps to identify and classify different associative algebras. |
| title | Hochschild cohomology groups of 5-dimensional complex nilpotent associative algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2512.09346 |