This talk is about the entropy of group actions of amenable groups. I will present recent progress on questions asked by Christopher Deninger about the entropy of certain principal algebraic dynamical systems. I will show that the entropy of an algebraic dynamical system agrees with the L2-torsion of the dual module over the integral group ring of the group acting. As a by-product we prove vanishing of the L2-torsion of amenable groups, which was conjectured by Wolfgang Luck. This is joint work with Hanfeng Li.