  Under some hypotheses (symmetry, confluence), we enumerate all quadratically
presented algebras, generated by creation and destruction operators, in which
number operators exist. We show that these are algebras of bosons, fermions,
their immediate generalizations that we call pseudo-bosons and pseudo-fermions,
and also matrix algebras, in the finitely generated case. We then recover
q-bosons (and pseudo-q-bosons) by a completion operation.
