Small non-associative division algebras up to isotopy

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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Date:2018
Main Author: Schwarz, Thomas
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Non-associative Division Algebras
Isotopy
17D99
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/625
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-625
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spelling oai:ojs.admjournal.luguniv.edu.ua: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
institution Algebra and Discrete Mathematics
collection OJS
language English
topic Non-associative Division Algebras
Isotopy
17D99
spellingShingle 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
work_keys_str_mv AT schwarzthomas smallnonassociativedivisionalgebrasuptoisotopy
first_indexed 2024-04-12T06:27:42Z
last_indexed 2024-04-12T06:27:42Z
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