Permutation-type solutions to the Yang-Baxter and other n-simplex equations

Details Permutation-type solutions to the Yang-Baxter and other n-simplex equations Permutation-type solutions to the Yang-Baxter and other n-simplex equations

1997-02-03

arxiv.org/abs/q-alg/9702006v3

Mathematics

Quantum Algebra

20 pages, LaTeX2e. to appear in J. Phys. A: Math. Gen. (1997)

Scientific paper

10.1088/0305-4470/30/13/024

We study permutation type solutions to n-simplex equations, that is, solutions whose R matrix can be written as a product of delta- functions depending linearly on the indices. With this ansatz the D^{n(n+1)} equations of the n-simplex equation reduce to an [n(n+1)/2+1]x[n(n+1)/2+1] matrix equation over Z_D. We have completely analyzed the 2-, 3- and 4-simplex equations in the generic D case. The solutions show interesting patterns that seem to continue to still higher simplex equations.

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