Geodesic
Spaces with polylinear forms
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 68-72.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider spaces with multilinear forms whose degree is greater than two. The motion groups of such spaces are subgroups of the general linear group whose transformations preserve the given multilinear form. The search for such groups becomes simpler if the multilinear form is defined on the linear space of some algebra and possesses the multiplicative property with respect to multiplication in this algebra. We prove that such a form exists in any associative algebra.
Keywords: linear algebra, associative algebra, multiplicative function, space with multilinear form, cyclic algebra. 
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N. I. Guseva; E. V. Lukyanova. Spaces with polylinear forms. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Geometry, and Combinatorics, Tome 215 (2022), pp. 68-72. http://geodesic.mathdoc.fr/item/INTO_2022_215_a6/

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