  We survey some of the known criteria for expansiveness of principal algebraic
actions of countably infinite discrete groups. In the special case of the
discrete Heisenberg group we propose a new approach to this problem based on
Allan's local principle.
  Furthermore, we present a first example of an absolutely summable homoclinic
point for a nonexpansive action of the discrete Heisenberg group and use it to
construct an equal-entropy symbolic cover of the system.
