An equivalence in generalized almost-Jordan algebras

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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Guzzo Jr,Henrique, Labra,Alicia
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2016
Materias:	Jordan algebras generalized almost-Jordan algebras Lie Triple algebras
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400011
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:scielo:S0716-09172016000400011
record_format	dspace
spelling	oai:scielo:S0716-091720160004000112017-01-05An equivalence in generalized almost-Jordan algebrasGuzzo Jr,HenriqueLabra,Alicia Jordan algebras generalized almost-Jordan algebras Lie Triple algebras 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, ifand only if A is an almost-Jordan or a Lie Triple algebra.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.35 n.4 20162016-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400011en10.4067/S0716-09172016000400011
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Jordan algebras generalized almost-Jordan algebras Lie Triple algebras
spellingShingle	Jordan algebras generalized almost-Jordan algebras Lie Triple algebras Guzzo Jr,Henrique Labra,Alicia An equivalence in generalized almost-Jordan algebras
description	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, ifand only if A is an almost-Jordan or a Lie Triple algebra.
author	Guzzo Jr,Henrique Labra,Alicia
author_facet	Guzzo Jr,Henrique Labra,Alicia
author_sort	Guzzo Jr,Henrique
title	An equivalence in generalized almost-Jordan algebras
title_short	An equivalence in generalized almost-Jordan algebras
title_full	An equivalence in generalized almost-Jordan algebras
title_fullStr	An equivalence in generalized almost-Jordan algebras
title_full_unstemmed	An equivalence in generalized almost-Jordan algebras
title_sort	equivalence in generalized almost-jordan algebras
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2016
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000400011
work_keys_str_mv	AT guzzojrhenrique anequivalenceingeneralizedalmostjordanalgebras AT labraalicia anequivalenceingeneralizedalmostjordanalgebras AT guzzojrhenrique equivalenceingeneralizedalmostjordanalgebras AT labraalicia equivalenceingeneralizedalmostjordanalgebras
_version_	1718439819157176320

An equivalence in generalized almost-Jordan algebras

Ejemplares similares