Non-commutative affine kinematic spaces and their automorphism group
As \textit{H. Karzel} and \textit{G. Kist} showed [J. Geom. 23, 124-127 (1984; Zbl 0558.51014)], any noncommutative pappian affine kinematic space can be described with the help of a near vector space. To investigate the automorphism groups of these kinematic spaces the author defines near- semilinear maps, namely maps between near vector spaces with the properties of semilinear maps. She shows that the set of automophisms of a noncommutative affine kinematic space is the group of all bijective near-semilinear maps of the belonging near vector space. For the special case of dimension 3 one gets that this groups is the semidirect product of the group of inner automorphisms with a product of linear maps and field automorphisms.
scientific article; zbMATH DE number 4036596