  The aim of this paper is to discuss a kinematical algebraic structure of a
theory of gravity, that would be unitary, renormalizable and coupled in the
same manner to both spinorial and tensorial matter fields. An analysis of the
common features as well as differences of the Yang-Mills theories and gauge
theories of gravity is carried out. In particular, we consider the following
issues: (i) Representations of the relevant global symmetry on states and on
fields, (ii) Relations between the relevant global and local symmetries, (iii)
Representations of the local symmetries on states and fields, (iv) Dimensional
analysis of the gauge algebra generators and the number of counter terms, and
(v) Coupling to the spinorial matter fields. We conclude, that various
difficulties on the gravity side can be overcome by considering the below
outlined Hypergravity gauge theory, that to some extend parallels the
string/membrane theories. This theory is based on an infinite Lie algebraic
structure of generators that transforms as "states" of the infinite-dimensional
irreducible representation of the $\bar{SL}(4,R)$ subgroup of the Group of
General Coordinate Transformations of R^4. The metric-affine and Poincar\'e
gauge theories of gravity are obtained through a spontaneous symmetry breaking
mechanism, with the metric field as nonlinear symmetry realizer.
