  We consider a generalization of the classical Laplace operator, which
includes the Laplace-Dunkl operator defined in terms of the
differential-difference operators associated with finite reflection groups
called Dunkl operators. For this Laplace-like operator, we determine a set of
symmetries commuting with it, which are generalized angular momentum operators,
and we present the algebraic relations for the symmetry algebra. In this
context, the generalized Dirac operator is then defined as a square root of our
Laplace-like operator. We explicitly determine a family of graded operators
which commute or anti-commute with our Dirac-like operator depending on their
degree. The algebra generated by these symmetry operators is shown to be a
generalization of the standard angular momentum algebra and the recently
defined higher rank Bannai-Ito algebra.
