The structure of the group of special automorphisms of the deformed group of diffeomorphisms

Abstract:
The geometrical structure of Riemannian space can be set with the help of the deformed group of diffeomorphisms, thus information about curvature of space is contained in the third order of expansion of the multiplication law. The structure of an infinite group of automorphisms of the deformed group of diffeomorphisms, related to parallel transports of the vector fields and its action on group manifold and tangent vectors are studied. There is a Riemann-Cristoffel curvature tensor among the structural functions of the group; a covariant derivative performs a role of one of the group generators. It is shown that the structural equations of such group coincide with structural equations of the curved space of the torsion-free affine connection with variable curvature.