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Octonionic Cayley spinors and E 6

Tevian Dray, Corinne A. Manogue (2010)

Commentationes Mathematicae Universitatis Carolinae

Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group E 6 , and of its subgroups. We are therefore led to a description of E 6 in terms of 3 × 3 octonionic matrices, generalizing previous results in the 2 × 2 case. Our treatment naturally includes a description of several important subgroups of E 6 , notably G 2 , F 4 , and (the double cover of) S O ( 9 , 1 ) . An interpretation of the actions...

On annihilators in Jordan algebras.

Antonio Fernández López (1992)

Publicacions Matemàtiques

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 Herstein's theorems relating modularity in A and A(+).

José A. Anquela (1992)

Extracta Mathematicae

In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal...

On the behaviour of Jordan-algebra norms on associative algebras

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

Studia Mathematica

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 results...

On the CR-structure of certain linear group orbits in infinite dimensions

Wilhelm Kaup (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

For large classes of complex Banach spaces (mainly operator spaces) we consider orbits of finite rank elements under the group of linear isometries. These are (in general) real-analytic submanifolds of infinite dimension but of finite CR-codimension. We compute the polynomial convex hull of such orbits  M explicitly and show as main result that every continuous CR-function on  M has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes to infinite...

On the Lebesgue decomposition of the normal states of a JBW-algebra

Jacques Dubois, Brahim Hadjou (1992)

Mathematica Bohemica

In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.

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