-orthograded quasimonocomposition algebras with one-dimensional null component.
Soit un corps local non archimédien de caractéristique résiduelle différente de et . Nous définissons strates semi-simples et caractères semi-simples pour le groupe exceptionnel à l’aide des objets analogues pour le groupe , des automorphismes de trialité et d’une correspondance de Glauberman. Nous construisons alors les types semi-simples associés et nous donnons des conditions suffisantes pour que ces types s’induisent irréductiblement, obtenant ainsi des représentations supercuspidales...
This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms...
In this note we introduce the concept of Cayley homomorphism which is closely related with those of composition algebra and normalized orthogonal multiplication. The key result shows the existence of certain types of Cayley homomorphisms for infinite dimension. As an application we prove the existence of left division infinite-dimensional complete normed real algebras with left unity.
We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation...
Nous obtenons une version explicite de la théorie de Bruhat-Tits pour les groupes exceptionnels de type sur un corps local. Nous décrivons chaque construction concrètement en termes de réseaux : l’immeuble, les appartements, la structure simpliciale, les schémas en groupes associés. Les appendices traitent de l’analogie avec les espaces symétriques réels et des espaces symétriques associés à réel et complexe.
Nous obtenons une version explicite de la théorie de Bruhat-Tits pour les groupes exceptionnels des type ou sur un corps local. Nous décrivons chaque construction concrètement en termes de réseaux : l’immeuble, les appartements, la structure simpliciale, les schémas en groupes associés.
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....
This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops.