Journal: | Proyecciones (Antofagasta) |
Database: | PERIÓDICA |
System number: | 000406129 |
ISSN: | 0716-0917 |
Authors: | Guzzo-Junior, Henrique1 Labra, Alicia2 |
Institutions: | 1Universidade de Sao Paulo, Instituto de Matematica e Estatistica, Sao Paulo. Brasil 2Universidad de Chile, Departamento de Matemáticas, Santiago de Chile. Chile |
Year: | 2016 |
Season: | Dic |
Volumen: | 35 |
Number: | 4 |
Pages: | 505-519 |
Country: | Chile |
Language: | Inglés |
Document type: | Artículo |
Approach: | Analítico |
English abstract | In this paper we work with the variety of commutative algebras satisfying the identity β((x2y)x − ((yx)x)x) + γ(x3y − ((yx)x)x)=0, where β, γ are scalars. They are called generalized almost-Jordan algebras. We prove that this variety is equivalent to the variety of commutative algebras satisfying (3β + γ)(Gy(x, z, t) − Gx(y, z, t)) + (β + 3γ)(J(x, z, t)y − J(y, z, t)x)=0, for all x, y, z, t ∈ A, where J(x, y, z)=(xy)z+(yz)x+(zx)y and Gx(y, z, t)=(yz, x, t)+(yt, x, z)+ (zt, x, y). Moreover, we prove that if A is a commutative algebra, then J(x, z, t)y = J(y, z, t)x, for all x, y, z, t ∈ A, if and only if A is a generalized almost-Jordan algebra for β = 1 and γ = −3, that is, A satisfies the identity (x2y)x + 2¡ (yx)x ¢ x − 3x3y = 0 and we study this identity. We also prove that if A is a commutative algebra, then Gy(x, z, t) = Gx(y, z, t), for all x, y, z, t ∈ A, if and only if A is an almost-Jordan or a Lie Triple algebra |
Disciplines: | Matemáticas |
Keyword: | Matemáticas puras, Algebra, Algebras de Jordan, Algebras de Lie |
Keyword: | Mathematics, Pure mathematics, Algebra, Jordan algebras, Lie algebras |
Full text: | Texto completo (Ver PDF) |