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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2408.08246 |
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| _version_ | 1866916562113396736 |
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| author | Alon, Gil Chapman, Adam Paran, Elad |
| author_facet | Alon, Gil Chapman, Adam Paran, Elad |
| contents | Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra H. We describe the "algebraic hull" of a point in H^n and prove it is a product of spheres. Using this description we give a new proof to a conjecture of Gori, Sarfatti and Vlacci. We also show that the main result of [2] does not extend to general division algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08246 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the geometry of zero sets of central quaternionic polynomials II Alon, Gil Chapman, Adam Paran, Elad Rings and Algebras Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra H. We describe the "algebraic hull" of a point in H^n and prove it is a product of spheres. Using this description we give a new proof to a conjecture of Gori, Sarfatti and Vlacci. We also show that the main result of [2] does not extend to general division algebras. |
| title | On the geometry of zero sets of central quaternionic polynomials II |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2408.08246 |