TemperleyLiebAlgebra

: the PLANAR perfect matchings — the diagrams you can draw in a rectangle without crossings. Dimension , the Catalan numbers.

WikipediaTemperley–Lieb algebra↗WikidataQ4060645↗

TemperleyLiebAlgebra(n)the Temperley–Lieb algebra on strands

Domain: Diagram algebras

Details

• Dimension = 1, 2, 5, 14, 42 — the Catalan numbers, and the reason non-crossing matchings and Dyck paths are the same objects
• Generated by the cup-caps , with , , and when
• Those relations are what the stacking rule produces — they are not imposed separately
• The home of the Jones polynomial, via the Markov trace on

Examples

See also: BrauerAlgebra, MotzkinAlgebra, Diagram