Some Results on the Klein Quadric Representation for a General Quantum Spacetime

Abstract

The Klein representation is a general quantum space-time. The aggregate consisting of all (n-1)-planes in the complex projective space P²ⁿ⁻¹ forms a manifold of dimension n². This space is complexified, compactified version of the quantum space-time. The quadric of PG(5,q), over its prime field GF(p) (the integers modulo p).defined by equation, X₀X₃+X₁X₄+X₂X₅=0 is called the Klein Quadric. In this paper, we give an embedding of Alpha and Beta Planes of the Klein Quadric.