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JOURNALS // Algebra and Discrete Mathematics // Archive

Algebra Discrete Math., 2010 Volume 9, Issue 1, Pages 103–108 (Mi adm23)

This article is cited in 4 papers

RESEARCH ARTICLE

Small non-associative division algebras up to isotopy

Thomas Schwarz, S.J.


Abstract: 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.

Keywords: Non-associative division algebras, isotopy.

MSC: 17D99

Received: 25.11.2006
Revised: 14.05.2010

Language: English



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