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

This article is cited in 2 scientific papers (total in 2 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.

Full text: PDF file (193 kB)

Bibliographic databases:
MSC: 17D99
Received: 25.11.2006
Revised: 14.05.2010
Language:

Citation: Thomas Schwarz, S.J., “Small non-associative division algebras up to isotopy”, Algebra Discrete Math., 9:1 (2010), 103–108

Citation in format AMSBIB
\Bibitem{Sch10}
\by Thomas Schwarz, S.J.
\paper Small non-associative division algebras up to isotopy
\jour Algebra Discrete Math.
\yr 2010
\vol 9
\issue 1
\pages 103--108
\mathnet{http://mi.mathnet.ru/adm23}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2676715}
\zmath{https://zbmath.org/?q=an:1233.17003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Falcon O.J., Falcon R.M., Nunez J., “Isotopism and Isomorphism Classes of Certain Lie Algebras Over Finite Fields”, Results Math., 71:1-2 (2017), 167–183  crossref  mathscinet  zmath  isi  scopus
    2. Falcon O.J., Falcon R.M., Nunez J., “Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension Up to Seven Over Finite Fields”, Results Math., 71:3-4 (2017), 1151–1166  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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