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A ℤ 4 3 -grading on a 56 -dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E

Diego Aranda-Orna, Alberto Elduque, Mikhail Kochetov (2014)

Commentationes Mathematicae Universitatis Carolinae

We describe two constructions of a certain ℤ 4 3 -grading on the so-called Brown algebra (a simple structurable algebra of dimension 56 and skew-dimension 1 ) over an algebraically closed field of characteristic different from 2 . The Weyl group of this grading is computed. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types E 6 , E 7 and E 8 .

A classification for real and complex finite dimensional ℱ * -algebras

Mauro Meschiari (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

La presente Nota contiene una lista di J ⋆ -algebre reali di dimensione finita ed una lista di J ⋆ -algebre complesse di dimensione finita tali che: 1) due elementi distinti di ogni lista non sono mai J ⋆ -isomorfi; 2) ogni J ⋆ -algebra di dimensione finita reale (complessa) è J ⋆ —isomorfa su 𝐑 (su 𝐂 ) alla somma diretta, finita, di J ⋆ -algebre reali (complesse) elencate nella lista. In altre parole, diamo qui una classificazione completa delle J ⋆ —algebre reali e delle J ⋆ -algebre complesse di dimensione finita. Nel...

A glimpse at the theory of Jordan-Banach triple systems.

José M. Isidro (1989)

Revista Matemática de la Universidad Complutense de Madrid

In this article, a survey of the theory of Jordan-Banach triple systems is presented. Most of the recent relevant results in this area have been included, though no proofs are given.

A non-semiprime associative algebra with zero weak radical.

Abdelfattah Haily (1997)

Extracta Mathematicae

The weak radical, W-Rad(A) of a non-associative algebra A, has been introduced by A. Rodríguez Palacios in [3] in order to generalize the Johnson's uniqueness of norm theorem to general complete normed non-associative algebras (see also [2] for another application of this notion). In [4], he showed that if A is a semiprime non-associative algebra with DCC on ideals, then W-Rad(A) = 0. In the first part of this paper we give an example of a non-semiprime associative algebra A with DCC on ideals and...

A structure theory for Jordan H * -pairs

A. J. Calderón Martín, C. Martín González (2004)

Bollettino dell'Unione Matematica Italiana

Jordan H * -pairs appear, in a natural way, in the study of Lie H * -triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie H * -triple systems is reduced to prove the existence of certain L * -algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan H * -pairs to a wide class of Lie H * -triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative H * -pairs, of...

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