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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.17881 |
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| _version_ | 1866917306525810688 |
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| author | Fretwell, Dan Roberts, Jenny |
| author_facet | Fretwell, Dan Roberts, Jenny |
| contents | We construct and investigate certain (unbalanced) superalgebra structures on $\text{End}_K(V)$, with $K$ a field of characteristic $0$ and $V$ a finite dimensional $K$-vector space (of dimension $n\geq 2$). These structures are induced by a choice of non-degenerate symmetric bilinear form $B$ on $V$ and a choice of non-zero base vector $w\in V$. After exploring the construction further, we apply our results to certain questions concerning integer matrix factorization and isometry of integral lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric bilinear forms, superalgebras and integer matrix factorization Fretwell, Dan Roberts, Jenny Rings and Algebras We construct and investigate certain (unbalanced) superalgebra structures on $\text{End}_K(V)$, with $K$ a field of characteristic $0$ and $V$ a finite dimensional $K$-vector space (of dimension $n\geq 2$). These structures are induced by a choice of non-degenerate symmetric bilinear form $B$ on $V$ and a choice of non-zero base vector $w\in V$. After exploring the construction further, we apply our results to certain questions concerning integer matrix factorization and isometry of integral lattices. |
| title | Symmetric bilinear forms, superalgebras and integer matrix factorization |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2404.17881 |