  A.A. Kirillov introduced the family algebras in 2000. In this paper we study
the noncommutative Poisson bracket P on the classical family algebra. We show
that P is the first-order deformation from the classical family algebra to the
quantum family algebra. We will prove that the noncommutative Poisson bracket
is in fact a Hochschild 2-coboundary therefore the deformation is
infinitesimally trivial. In the last part of this paper we also talk about
Mackey's analogue and the quantization problem of the family algebras.
