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$ℤ_{3}$ -orthograded quasimonocomposition algebras with one-dimensional null component.

Gaĭnov, A.T. (2005)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

$ℤ_{n}$ -ортоградуированные монокомпозиционные алгебры.

А.Т. Гайнов (2002)

Algebra i Logika

Caractères semi-simples de $G_{2} (F)$ , $F$ corps local non archimédien

Laure Blasco, Corinne Blondel (2012)

Annales scientifiques de l'École Normale Supérieure

Soit $F$ un corps local non archimédien de caractéristique résiduelle différente de $2$ et $3$ . Nous définissons strates semi-simples et caractères semi-simples pour le groupe exceptionnel $G_{2} (F)$ à l’aide des objets analogues pour le groupe $SO (8, F)$ , 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...

Irreducible binary $(- 1, 1)$ -bimodules over simple finite-dimensional algebras.

Pchelintsev, S.V. (2006)

Sibirskij Matematicheskij Zhurnal

Lattice isomorphisms of alternative algebras

Jesús A. Laliena (1988)

Extracta Mathematicae

Morphisms in the category of finite-dimensional absolute valued algebras

Seidon Alsaody (2011)

Colloquium Mathematicae

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...

Multiplikation in euklidischen Räumen.

Werner Bos (1971/1972)

Jahresbericht der Deutschen Mathematiker-Vereinigung

Nonassociative algebras: a framework for differential geometry.

Ionescu, Lucian M. (2003)

International Journal of Mathematics and Mathematical Sciences

Nonassociative algebras with submultiplicative bilinear form.

Cedilnik, A., Zalar, B. (1994)

Acta Mathematica Universitatis Comenianae. New Series

On one-sided division infinite-dimensional normed real algebras.

José Antonio Cuenca Mira (1992)

Publicacions Matemàtiques

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.

On the dimension of a composition algebra.

Rost, Markus (1996)

Documenta Mathematica

One-sided division absolute valued algebras.

Ana Rodríguez Palacios (1992)

Publicacions Matemàtiques

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...

Pseudo-composition algebras.

Kurt Meyberg, J. Marshall Osborn (1993)

Mathematische Zeitschrift

Schémas en groupes et immeubles des groupes exceptionnels sur un corps local. Première partie : le groupe $G_{2}$

Wee Teck Gan, Jiu-Kang Yu (2003)

Bulletin de la Société Mathématique de France

Nous obtenons une version explicite de la théorie de Bruhat-Tits pour les groupes exceptionnels de type $G_{2}$ 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 $G_{2}$ réel et complexe.

Schémas en groupes et immeubles des groupes exceptionnels sur un corps local. Deuxième partie : les groupes $F_{4}$ et $E_{6}$

Wee Teck Gan, Jiu-Kang Yu (2005)

Bulletin de la Société Mathématique de France

Nous obtenons une version explicite de la théorie de Bruhat-Tits pour les groupes exceptionnels des type $F_{4}$ ou $E_{6}$ 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.

Some equations in algebras obtained by the Cayley-Dickson process.

Flaut, Cristina (2001)

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

Some properties of octonion and quaternion algebras.

Flaut, Cristina (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Some properties of the composition algebras.

Flaut, Cristina (2003)

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

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)

Commentationes Mathematicae Universitatis Carolinae

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 $𝔽 S_{n}$ of the symmetric group $S_{n}$ over a field $𝔽$ of characteristic 0 (or $p > n$ ). The goal is to obtain a constructive version of the isomorphism $ψ : ⨁_{λ} M_{d_{λ}} (𝔽) ⟶ 𝔽 S_{n}$ where $λ$ is a partition of $n$ and $d_{λ}$ counts the standard tableaux of shape $λ$ ....

Subloops of sedenions

Benard M. Kivunge, Jonathan D. H Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

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.

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