Representation theory and an isomorphism theorem for the Framisation of the Temperley-Lieb algebra

2015/03/11 by Maria Chlouveraki, Chlouveraki, Maria, Guillaume Pouchin +1 · 1 citation
Mathematics · #05E10 #16S80 #20C08 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1503.03396

openalex publication_date 2015/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we describe the irreducible representations and give a dimension formula for the Framisation of the Temperley-Lieb algebra. We then prove that the Framisation of the Temperley-Lieb algebra is isomorphic to a direct sum of matrix algebras over tensor products of classical Temperley-Lieb algebras. This allows us to construct a basis for it. We also study in a similar way the Complex Reflection Temperley-Lieb algebra.

Citations

• Identifying the invariants for classical knots and links from the\n Yokonuma-Hecke algebras

Cited by

• Framization of a Temperley-Lieb algebra of type \mathttB

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