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Representation theory and an isomorphism theorem for the framisation of the Temperley–Lieb algebra

2016; Springer Science+Business Media; Volume: 285; Issue: 3-4 Linguagem: Inglês

10.1007/s00209-016-1751-5

1432-1823

Maria Chlouveraki, Guillaume Pouchin,

Advanced Operator Algebra Research

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.