Let Wn (R) be the Weyl algebra of index n. We have shown that by using extension and localization, it is possible to construct homomorphisms of Wn (R) onto its image in a localization, or a quotient thereof, of U(so(2, q)), the universal enveloping algebra of so(2, q), forn depending upon q . Here we treat the so(2, 1) case in complete detail. We establish an isomorphism of skew fields, specifically, D(so(2, 1)) ~ D(1,1)(R) where D1,1(R) is the fraction field of W1.1(R) ~ W1(R) ⊗ R(y) with R(y) being the ring of polynomials in the indeterminate y and D(so(2, 1)) is a certain extension of the skew field of fractions of U(so(2, 1)), which is described below. We give applications of this result to representations. In particular we are able to construct representations of W1 (R) out of representations of so (2, 1). Thus, we are able, for this lowest dimensional case, to obtain the canonical commutation relations and representations of them out of so(2, 1) symmetry. Using similar results in higher dimensions  we are able to construct representations of Wn(R) out of representations of so (2, q).