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type kinetic terms). It turns out that two different theories exist in the first order formulation, both SU(1,4) 0 U(1) gauge invariant and supersymmetric. Going to the second order formalism the two theories become identical and the spin 1 kinetic term is generated. The dichotomy present in the first order version of the theory may be of some importance for quantization. The introduction of a cosmological constant and the reintroduction of the noncontracted group SU(2, 2/l) is trivial in this approach as in N = 1 supergravity. At the end of the paper we explicitly exhibit the de Sitter version of the theory. It must be noted that this is only the second example of a completely pure geometrical supersymmetric theory known to date. By pure we mean that no other field except the Lie Algebra valued lform potential is needed.
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In this paper an algebraic approach to canonical quantization on indefinite inner product space is presented. Concrete realization of such quantization of given classical system described by a symplectic space (M. a) is obtained by means of so called ./\*-representation of CCR algebra d(M, 0). So-ca