Homomorphisms of Jordan algebras and homomorphisms of projective planes

Elena Brožíková

Displaying similar documents to “Homomorphisms of Jordan algebras and homomorphisms of projective planes”

The Jordan structure of CSL algebras

Fangyan Lu (2009)

Studia Mathematica

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We show that every Jordan isomorphism between CSL algebras is the sum of an isomorphism and an anti-isomorphism. Also we show that each Jordan derivation of a CSL algebra is a derivation.

The geometry of null systems, Jordan algebras and von Staudt's theorem

Wolfgang Bertram (2003)

Annales de l’institut Fourier

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We characterize an important class of generalized projective geometries $(X, X^{'})$ by the following essentially equivalent properties: (1) $(X, X^{'})$ admits a central null-system; (2) $(X, X^{'})$ admits inner polarities: (3) $(X, X^{'})$ is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue...

Holomorphic functional calculus in Jordan-Banach algebras

J. Martinez Moreno (1991)

Annales scientifiques de l'Université de Clermont. Mathématiques

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On annihilators in Jordan algebras.

Antonio Fernández López (1992)

Publicacions Matemàtiques

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In this paper we prove that a nondegenerate Jordan algebra satisfying the descending chain condition on the principal inner ideals, also satisfies the ascending chain condition on the annihilators of the principal inner ideals. We also study annihilators in Jordan algebras without nilpotent elements and in JB-algebras.

On the behaviour of Jordan-algebra norms on associative algebras

Miguel Cabrera Garcia, Antonio Moreno Galindo, Angel Rodríguez Palacios (1995)

Studia Mathematica

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We prove that for a suitable associative (real or complex) algebra which has many nice algebraic properties, such as being simple and having minimal idempotents, a norm can be given such that the mapping (a,b) ↦ ab + ba is jointly continuous while (a,b) ↦ ab is only separately continuous. We also prove that such a pathology cannot arise for associative simple algebras with a unit. Similar results are obtained for the so-called "norm extension problem", and the relationship between these...

The triple-norm extension problem: the nondegenerate complete case.

A. Moreno Galindo (1999)

Studia Mathematica

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We prove that, if A is an associative algebra with two commuting involutions τ and π, if A is a τ-π-tight envelope of the Jordan Triple System T:=H(A,τ) ∩ S(A,π), and if T is nondegenerate, then every complete norm on T making the triple product continuous is equivalent to the restriction to T of an algebra norm on A.

The norm extension problem: positive results and limits.

A. Moreno Galindo, A. Rodríguez Palacios (1997)

Extracta Mathematicae

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Distinguishing Jordan polynomials by means of a single Jordan-algebra norm

A. Moreno Galindo (1997)

Studia Mathematica

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For = ℝ or ℂ we exhibit a Jordan-algebra norm ⎮·⎮ on the simple associative algebra $M_{\infty} ()$ with the property that Jordan polynomials over are precisely those associative polynomials over which act ⎮·⎮-continuously on $M_{\infty} ()$ . This analytic determination of Jordan polynomials improves the one recently obtained in [5].