Moufang loops and alternative algebras-Reference-Cited by-同舟云学术

Moufang loops and alternative algebras

Published:2003-08-28 Issue:2 Volume:132 Page:313-316
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Shestakov Ivan

Abstract

Let O \mathbf {O} be the algebra O \mathbf {O} of classical real octonions or the (split) algebra of octonions over the finite field G F ( p 2 ) , p > 2 GF(p^2),\ p>2 . Then the quotient loop O ∗ / Z ∗ \mathbf {O}^*/Z^* of the Moufang loop O ∗ \mathbf {O}^* of all invertible elements of the algebra O \mathbf {O} modulo its center Z ∗ Z^* is not embedded into a loop of invertible elements of any alternative algebra.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2004-132-02/S0002-9939-03-07260-5/S0002-9939-03-07260-5.pdf

Reference6 articles.

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3. R. Moufang, Zur Structur von Alternativekörpern, Math. Ann. 110 (1935), 416–430.

4. G. B. Nagy, Applications of Bol reflections, Ph.D. Dissertation, Szeged (Hungary), 1999.

5. N. Sandu, About the embedding of Moufang loops in alternative algebras, Loops ’99 Conference, July 27, 1999–Aug. 1, 1999, Prague, Abstracts, 33-34.

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