Small non-associative division algebras up to isotopy
We classify small, non-associative division algebras up to isotopy. We reduce the classification problem to an involved case distinction that a computer program can solve. As a result, we classify algebras with 4, 8, 16, and 9 elements. In particular, we show that non-associative division algebras...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/625 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-625 |
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admjournalluguniveduua-article-6252018-04-04T08:18:32Z Small non-associative division algebras up to isotopy Schwarz, Thomas Non-associative Division Algebras, Isotopy 17D99 We classify small, non-associative division algebras up to isotopy. We reduce the classification problem to an involved case distinction that a computer program can solve. As a result, we classify algebras with 4, 8, 16, and 9 elements. In particular, we show that non-associative division algebras of size 4, 8, and 9 are isotopes of a Galois field, whereas there are three isotopy classes of division algebras with 16 elements. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/625 Algebra and Discrete Mathematics; Vol 9, No 1 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/625/160 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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2018-04-04T08:18:32Z |
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OJS |
| language |
English |
| topic |
Non-associative Division Algebras Isotopy 17D99 |
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Non-associative Division Algebras Isotopy 17D99 Schwarz, Thomas Small non-associative division algebras up to isotopy |
| topic_facet |
Non-associative Division Algebras Isotopy 17D99 |
| format |
Article |
| author |
Schwarz, Thomas |
| author_facet |
Schwarz, Thomas |
| author_sort |
Schwarz, Thomas |
| title |
Small non-associative division algebras up to isotopy |
| title_short |
Small non-associative division algebras up to isotopy |
| title_full |
Small non-associative division algebras up to isotopy |
| title_fullStr |
Small non-associative division algebras up to isotopy |
| title_full_unstemmed |
Small non-associative division algebras up to isotopy |
| title_sort |
small non-associative division algebras up to isotopy |
| description |
We classify small, non-associative division algebras up to isotopy. We reduce the classification problem to an involved case distinction that a computer program can solve. As a result, we classify algebras with 4, 8, 16, and 9 elements. In particular, we show that non-associative division algebras of size 4, 8, and 9 are isotopes of a Galois field, whereas there are three isotopy classes of division algebras with 16 elements. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/625 |
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AT schwarzthomas smallnonassociativedivisionalgebrasuptoisotopy |
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2025-12-02T15:36:19Z |
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2025-12-02T15:36:19Z |
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1850411350653665280 |