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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154498 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Small non-associative division algebras up to isotopy / T. Schwarz // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 1. — С. 103–108. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862545770061758464 |
|---|---|
| author | Schwarz, T. |
| author_facet | Schwarz, T. |
| citation_txt | Small non-associative division algebras up to isotopy / T. Schwarz // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 1. — С. 103–108. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-25T07:17:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154498 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T07:17:53Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Schwarz, T. 2019-06-15T16:10:47Z 2019-06-15T16:10:47Z 2010 Small non-associative division algebras up to isotopy / T. Schwarz // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 1. — С. 103–108. — Бібліогр.: 4 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:17D99. https://nasplib.isofts.kiev.ua/handle/123456789/154498 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Small non-associative division algebras up to isotopy Article published earlier |
| spellingShingle | Small non-associative division algebras up to isotopy Schwarz, T. |
| title | 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_short | Small non-associative division algebras up to isotopy |
| title_sort | small non-associative division algebras up to isotopy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154498 |
| work_keys_str_mv | AT schwarzt smallnonassociativedivisionalgebrasuptoisotopy |