  We present the properties of new Dirac-type operators generated by real or
complex-valued special Killing-Yano tensors that are covariantly constant and
represent roots of the metric tensor. In the real case these are just the so
called complex or hyper-complex structures of the K\" ahlerian manifolds. Such
a Killing-Yano tensor produces simultaneously a Dirac-type operator and the
generator of a one-parameter Lie group connecting this operator with the
standard Dirac one. In this way the Dirac operators are related among
themselves through continuous transformations associated with specific discrete
ones. We show that the group of these continuous transformations can be only
U(1) or SU(2). It is pointed out that the Dirac and Dirac-type operators can
form N=4 superalgebras whose automorphisms combine isometries with the SU(2)
transformation generated by the Killing-Yano tensors. As an example we study
the automorphisms of the superalgebras of Dirac operators on Minkowski
spacetime.
