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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Moufang loops and alternative algebras


Author: Ivan P. Shestakov
Journal: Proc. Amer. Math. Soc. 132 (2004), 313-316
MSC (2000): Primary 17D05, 20N05
Published electronically: August 28, 2003
MathSciNet review: 2022350
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Abstract: Let $\mathbf{O}$ be the algebra $\mathbf{O}$ of classical real octonions or the (split) algebra of octonions over the finite field $GF(p^2), p>2$. Then the quotient loop $\mathbf{O}^*/Z^*$ of the Moufang loop $\mathbf{O}^*$ of all invertible elements of the algebra $\mathbf{O}$ modulo its center $Z^*$ is not embedded into a loop of invertible elements of any alternative algebra.


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Additional Information

Ivan P. Shestakov
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 - CEP 05315-970, São Paulo, Brazil and Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
Email: shestak@ime.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07260-5
PII: S 0002-9939(03)07260-5
Keywords: Moufang loop, alternative algebra
Received by editor(s): January 2, 2002
Published electronically: August 28, 2003
Additional Notes: Partially supported by CNPq grant 300528/99-0
Communicated by: Lance W. Small
Article copyright: © Copyright 2003 American Mathematical Society