  We study a class of duality transformations in generalised Z(2) gauge
theories and Ising models on two- and three-dimensional compact lattices. The
theories are interpreted algebraically in terms of the structure constants of a
bidimensional vector space H with algebra and coalgebra structures, and it is
shown that for any change of basis in H there is a related symmetry between
such models. The classical Kramers and Wannier dualities are described as
special cases of these transformations. We derive explicit expressions for the
relation between partition functions on general finite triangulations for these
cases, extending results known for square and cubic lattices in the
thermodynamical limit. A class of symmetry transformations in which the gauge
coupling changes continuously is also studied in two dimensions.
