| Revista: | Proyecciones (Antofagasta) |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000406129 |
| ISSN: | 0716-0917 |
| Autores: | Guzzo-Junior, Henrique1 Labra, Alicia2 |
| Instituciones: | 1Universidade de Sao Paulo, Instituto de Matematica e Estatistica, Sao Paulo. Brasil 2Universidad de Chile, Departamento de Matemáticas, Santiago de Chile. Chile |
| Año: | 2016 |
| Periodo: | Dic |
| Volumen: | 35 |
| Número: | 4 |
| Paginación: | 505-519 |
| País: | Chile |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Analítico |
| Resumen en inglés | 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 |
| Disciplinas: | Matemáticas |
| Palabras clave: | Matemáticas puras, Algebra, Algebras de Jordan, Algebras de Lie |
| Keyword: | Mathematics, Pure mathematics, Algebra, Jordan algebras, Lie algebras |
| Texto completo: | Texto completo (Ver PDF) |
