  We consider the compatibility conditions for a N-particle D-dimensional
Wigner quantum oscillator. These conditions can be rewritten as certain triple
relations involving anticommutators, so it is natural to look for solutions in
terms of Lie superalgebras. In the recent classification of ``generalized
quantum statistics'' for the basic classical Lie superalgebras
[math-ph/0504013], each such statistics is characterized by a set of creation
and annihilation operators plus a set of triple relations. In the present
letter, we investigate which cases of this classification also lead to
solutions of the compatibility conditions. Our analysis yields some known
solutions and several classes of new solutions.
