A classification of the division algebras that are isotopic to a cyclic Galois field extension
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916632367988736 |
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| author | Pumpluen, Susanne |
| author_facet | Pumpluen, Susanne |
| contents | We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The classification is ``tight'' in the sense that the list of algebras has features that make it easy to distinguish non-isomorphic ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A classification of the division algebras that are isotopic to a cyclic Galois field extension Pumpluen, Susanne Rings and Algebras We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The classification is ``tight'' in the sense that the list of algebras has features that make it easy to distinguish non-isomorphic ones. |
| title | A classification of the division algebras that are isotopic to a cyclic Galois field extension |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2407.11598 |