Geometry of cyclic and anticyclic spaces

N. I. Guseva<sup>ab

a</sup> Moscow State Pedagogical University
^b All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow

Abstract: We consider spaces whose geometry is determined by forms that are not quadratic. These forms are related to cyclic and anticyclic linear algebras. We describe linear transformations that preserve these forms and indicate invariants of these transformations similar to the distance between points and the angle between vectors.

Keywords: space with a multilinear form, cyclic algebra, cyclic space, anticyclic space.

UDC: 512.6

MSC: 15A66, 15A69, 16S38

DOI: 10.36535/0233-6723-2023-222-10-18