FLIP-MOVES AND GRADED ASSOCIATIVE ALGEBRAS

The relation between discrete topological field theories on triangulat ions of two-dimensional manifolds and associative algebras was worked out recently. The starting point for this development was the graphica l interpretation of the associativity as flip of triangles. We show th at there is a more general relation between dip-moves with two n-gons and Z(n-2)-graded associative algebras. A detailed examination shows t hat flip-invariant models on a lattice of n-gons can be constructed fr om Z(2)- or Z(1)-graded algebras, reducing in the second case to trian gulations of the two-dimensional manifolds. Related problems occur nat urally in three-dimensional topological lattice theories.