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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 Characterization of the State Space of Quantum Mechanics

Huzihiro Araki (1980)

Recherche Coopérative sur Programme n°25

A class of Lie and Jordan algebras realized by means of the canonical commutation relations

Hans Tilgner (1971)

Annales de l'I.H.P. Physique théorique

A classification for real and complex finite dimensional $\mathcal{F}^{*}$ -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 $J^{\star}$ -algebre reali di dimensione finita ed una lista di $J^{\star}$ -algebre complesse di dimensione finita tali che: 1) due elementi distinti di ogni lista non sono mai $J^{\star}$ -isomorfi; 2) ogni $J^{\star}$ -algebra di dimensione finita reale (complessa) è $J^{\star}$ —isomorfa su $\mathbf{R}$ (su $\mathbf{C}$ ) alla somma diretta, finita, di $J^{\star}$ -algebre reali (complesse) elencate nella lista. In altre parole, diamo qui una classificazione completa delle $J^{\star}$ —algebre reali e delle $J^{\star}$ -algebre complesse di dimensione finita. Nel...

A Generalized Hecke Identity.

Jean-Luis Clerc (2000)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

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 Holomorphic Characterization of Jordan C*-Algebras.

Wilhelm Kaup, Harald Upmeier, Robert Braun (1978)

Mathematische Zeitschrift

A Lie product type formula in Euclidean Jordan algebras

Jiyuan Tao (2016)

Special Matrices

In this paper,we state and prove an analog of Lie product formula in the setting of Euclidean Jordan algebras.

A new order relation for JB-algebras

Consuelo Martinez Lopez (1991)

Annales scientifiques de l'Université de Clermont. Mathématiques

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 note on Jordan automorphisms

H. Roos (1985)

Annales de l'I.H.P. Physique théorique

A note on Jordan rings of quotients

Pedro Jimenez Garijo (1991)

Annales scientifiques de l'Université de Clermont. Mathématiques

A Note on the Bidual of a JB-Algebra.

Harald Hanche-Olsen (1980)

Mathematische Zeitschrift

A note on the number of generators of a nodal algebra

Rich, Michael (1973)

Portugaliae mathematica

A pair of Jordan triple systems of Jordan pair type.

Asadurian, Eduard (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

A proof of the Russo-Dye theorem for $J B^{*}$ -algebras.

Siddiqui, Akhlaq A. (2010)

The New York Journal of Mathematics [electronic only]

A Riemann Mapping Theorem for Bounded Symmetric Domains in Complex Banach Spaces.

Wilhelm Kaup (1983)

Mathematische Zeitschrift

A spectral characterization of the socle of Banach Jordan systems.

Gerald Hessenberger (1996)

Mathematische Zeitschrift

A spectral theory for order unit spaces

M. C. Abbati, A. Manià (1981)

Annales de l'I.H.P. Physique théorique

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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