Flip-Moves and Graded Associative Algebras

Details Flip-Moves and Graded Associative Algebras Flip-Moves and Graded Associative Algebras

1994-07-15

arxiv.org/abs/hep-th/9407083v1

J.Phys. A28 (1995) 3117-3128

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX, Freiburg Preprint THEP 94/6

Scientific paper

10.1088/0305-4470/28/11/014

The relation between discrete topological field theories on triangulations of two-dimensional manifolds and associative algebras was worked out recently. The starting point for this development was the graphical interpretation of the associativity as flip of triangles. We show that there is a more general relation between flip-moves with two $n$-gons and $Z_{n-2}$-graded associative algebras. A detailed examination shows that flip-invariant models on a lattice of $n$-gons can be constructed {}from $Z_{2}$- or $Z_{1}$-graded algebras, reducing in the second case to triangulations of the two-dimensional manifolds. Related problems occure naturally in three-dimensional topological lattice theories.

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