CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD-Reference-Cited by-同舟云学术

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

Published:2010-10 Issue:05 Volume:09 Page:791-808
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

GRISHKOV ALEXANDER N.¹,GIULIANI MARIA DE LOURDES MERLINI²,ZAVARNITSINE ANDREI V.³

Affiliation:

1. Departamento de Matemática, Universidade de São Paulo, Caixa Postal 66281, São Paulo-SP, 05311-970, Brasil

2. Departamento de Matemática, Universidade Federal de Santa Maria, Santa Maria-RS, Brasil

3. Sobolev Institute of Mathematics, Koptyug av. 4, Novosibirsk, 630090, Russia

Abstract

We classify all unital subalgebras of the Cayley algebra 𝕆(q) over the finite field Fq, q = pn. We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of 𝕆(q). We also determine the structure of the Moufang loops associated with each subalgebra of 𝕆(q).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498810004233

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