Spaces with polylinear forms

Abstract

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.