21-Parameter Poincare Group in Six-dimensional Space-Time

The homogeneous Lorentz transformations in terms of 6x6 antisymmetric transformation matrix have been derived in six-dimensional space-time. The infinitesimal generators of Lorentz group and their commutation relations have been identified in vector representation of generators. The commutation relations and invariant operators of Homogeneous Lorentz group have been shown to confine in their representation space. The commutation relations of generator matricesfor twenty-one parameter inhomogeneous Lorentz Group in six-spacedo inherit space-time subspaces, which are necessarily structured in six-space. Constructing operators for Poincare Group, it has been shown that the operator relations choose specific space-time selection and unitary representation of operators in six-dimensional space time, D(3??3)is same as in observable four-dimensional Minkowski space [R^4]?D(3??1).