Geodesic
Small non-associative division algebras up to isotopy
Algebra and discrete mathematics, Tome 9 (2010) no. 1, pp. 103-108

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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: isotopy.
Mots-clés : Non-associative division algebras 
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     title = {Small non-associative division algebras up to isotopy},
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Thomas Schwarz; S.J. Small non-associative division algebras up to isotopy. Algebra and discrete mathematics, Tome 9 (2010) no. 1, pp. 103-108. http://geodesic.mathdoc.fr/item/ADM_2010_9_1_a8/