Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras

• Autorzy: M. Brešar , M. Cabrera , M. Fošner , A. R. Villena
• Języki publikacji: EN

Abstrakty

EN

A linear subspace M of a Jordan algebra J is said to be a Lie triple ideal of J if [M,J,J] ⊆ M, where [·,·,·] denotes the associator. We show that every Lie triple ideal M of a nondegenerate Jordan algebra J is either contained in the center of J or contains the nonzero Lie triple ideal [U,J,J], where U is the ideal of J generated by [M,M,M].
Let H be a Jordan algebra, let J be a prime nondegenerate Jordan algebra with extended centroid C and unital central closure Ĵ, and let Φ: H → J be a Lie triple epimorphism (i.e. a linear surjection preserving associators). Assume that deg(J) ≥ 12. Then we show that there exist a homomorphism Ψ: H → Ĵ and a linear map τ: H → C satisfying τ([H,H,H]) = 0 such that either Φ = Ψ + τ or Φ = -Ψ + τ.
Using the preceding results we show that the separating space of a Lie triple epimorphism between Jordan-Banach algebras H and J lies in the center modulo the radical of J.

Kategorie tematyczne

• 17C10: Structure theory
• 46H70: Nonassociative topological algebras
• 46H40: Automatic continuity
• 17C65: Jordan structures on Banach spaces and algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 169
• Numer: 3
• Strony: 207-228

Daty

wydano

2005

Twórcy

autor

M. Brešar

• Department of Mathematics, University of Maribor, PEF, Koroška 160, 2000 Maribor, Slovenia

autor

M. Cabrera

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

autor

M. Fošner

• Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia

autor

A. R. Villena

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm169-3-1