  Examples of (strongly continuous) one-parameter groups of automorphisms of
UHF C*-algebras are given. One example has the property that the infinitesimal
generator does not have a union of finite-dimensional subalgebras as a core.
(This solves the so-called core problem, raised by S. Sakai, in the negative.)
The other has the property of not being classical or commutative, i.e., the
one-parameter group is not just an inner perturbation of a one-parameter group
which has an increasing sequence of invariant finite-dimensional subalgebras
with dense union. (This was certainly expected but has not been proven
explicitly.)
