  We discuss questions pertaining to the definition of `momentum', `momentum
space', `phase space', and `Wigner distributions'; for finite dimensional
quantum systems. For such systems, where traditional concepts of `momenta'
established for continuum situations offer little help, we propose a physically
reasonable and mathematically tangible definition and use it for the purpose of
setting up Wigner distributions in a purely algebraic manner. It is found that
the point of view adopted here is limited to odd dimensional systems only. The
mathematical reasons which force this situation are examined in detail.
