Graded cellular bases for Temperley-Lieb algebras of type A and B

2012/03/12 by David Plaza, Plaza, David, Steen Ryom-Hansen +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1203.2592

openalex publication_date 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Temperley-Lieb algebra of type A and the blob algebra (also known as the Temperley-Lieb algebra of type B) at roots of unity are \mathbb Z-graded algebras.We moreover show that they are graded cellular algebras, thus making their cell modules, or standard modules, graded modules for the algebras.

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