Markov elements in affine Temperley-Lieb algebras

2015/01/27 by Sadek Al Harbat, Harbat, Sadek Al
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1501.06756

openalex publication_date 2015/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a tower of affine Temperley-Lieb algebras of type A_n and we define Markov elements in those algebras. We prove that any trace over an affine Temperley-Lieb algebras of type A₂ is uniquely defined by its values on the Markov elements.

Related

• Markov trace on a tower of affine Temperley-Lieb algebras of type A_n
• On the Markov trace for Temperley--Lieb algebras of type E_n
• Framization of a Temperley-Lieb algebra of type \mathttB
• Uncoiled affine Temperley-Lieb algebras and their Wenzl-Jones projectors
• The Yokonuma-Temperley-Lieb Algebra