Standard monomials for temperley-lieb algebras

Sungsoon Kim (1) , Dong-Il Lee

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We deal with Temperley-Lieb algebras of type B, extending the result in [3, §6]. By completing the relations coming from a presentation of the Temperley-Lieb algebra, we find its Gröbner-Shirshov basis to obtain the corresponding set of standard monomials. The explicit multiplication table between the monomials follows naturally.

Domaines: Mathématiques [math]

Sungsoon Kim, Dong-Il Lee. Standard monomials for temperley-lieb algebras. ACM Communications in Computer Algebra, 2017, 50 (4), pp.179-181. ⟨10.1145/3055282.3055296⟩. ⟨hal-03882001⟩