  A few things are known, and many are unknown, on the automorphism group of
the free MV-algebra over n-1 generators. In this paper we show that this group
appears as the stabilizer of 1 in the larger group of all automorphisms of the
free cancellative hoop over n generators. Both groups have a dual action on the
same space, namely the (n-1)-dimensional cube. The larger group has a richer
dynamics, at the expense of loosing the two key features of the McNaughton
homeomorphisms: preservation of denominators of rational points, and
preservation of the Lebesgue measure. We present here some basic results, some
examples, and some problems.
