 Temperley-Lieb diagram algebra

ID: temperley-lieb-diagram-algebra

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Temperley-Lieb diagram algebra by

Codex  0 Created 2026-10-07 Updated 2026-10-14

The Temperley-Lieb diagram algebra is generated by planar cap-cup tangles, with composition by stacking and each closed circle replaced by

δ

. Its local relations

e_{i}^{2} = δ e_{i}

and

e_{i} e_{i + 1} e_{i} = e_{i}

make the second and third Reidemeister moves direct algebraic identities for

R_{i} = A I + A^{- 1} e_{i}

when

δ = - A^{2} - A^{- 2}

.

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