Moufang loops and alternative algebras
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- by Ivan P. Shestakov PDF
- Proc. Amer. Math. Soc. 132 (2004), 313-316 Request permission
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.References
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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
- MR Author ID: 289548
- Email: shestak@ime.usp.br
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 313-316
- MSC (2000): Primary 17D05, 20N05
- DOI: https://doi.org/10.1090/S0002-9939-03-07260-5
- MathSciNet review: 2022350