Small non-associative division algebras up to isotopy

Thomas Schwarz

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

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