## Abstract

The Temperley–Lieb algebra is a finite-dimensional associative algebra that arose in the context of statistical mechanics and occurs naturally as a quotient of the Hecke algebra arising from a Coxeter group of type A. It is often realized in terms of a certain diagram algebra, where every diagram can be written as a product of “simple diagrams”. These factorizations correspond precisely to factorizations of the so-called fully commutative elements of the Coxeter group that index a particular basis. Given a reduced factorization of a fully commutative element, it is straight-forward to construct the corresponding diagram. On the other hand, it is generally difficult to reconstruct the factorization given an arbitrary diagram. We present an efficient algorithm for obtaining a reduced factorization for a given diagram.

Original language | English (US) |
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Pages (from-to) | 89-108 |

Number of pages | 20 |

Journal | Involve |

Volume | 10 |

Issue number | 1 |

DOIs | |

State | Published - 2017 |

## Keywords

- Coxeter group
- Temperley–Lieb algebra
- diagram algebra
- heap

## ASJC Scopus subject areas

- General Mathematics