Geometrical equivalence and action type geometrical equivalence of group representations

Abstract

In the present work, we deal with concepts of geometrical equivalence of universal algebras. We concentrate our attention on geometrical equivalence of group representations. In this case one can speak about (full) geometrical equivalence and two partial cases: group geometrical equivalence and action-type geometrical equivalence. Our work has two main goals. The first one is to study geometrical equivalence of group representations via group and action-type geometrical equivalences. The second goal is to give an example which proves that we can not conclude the geometrical equivalence of group representations from the corresponding action-type geometrical equivalence and group geometrical equivalence.