Temperley-Lieb algebra

In statistical mechanics, the Temperley-Lieb algebra is an algebra generated by certain transfer matrix, invented by Temperley and Lieb in about 1971. It is also related to knot theory, the braid group, and subfactors of von Neumann algebras.

=Definition=

The Temperley-Lieb algebra is generated by elements e n for n ≥1 subject to the following relations:

e n 2= e n

e m e n = e n e m if | m - n |>1.

e n+1 e n e n+1 = τ e n+1

e n e n+1 e n = τ e n

=Further reading=

*N. Temperley, E. Lieb, [http://www.jstor.org/search/BasicSearchsi=1&hp=25&Search=Search&Query=temperley+lieb+percolation Relations between the percolation and colouring problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the precolation problem .] Proceedings of the Royal Society Series A 322 (1971), 251-280.