Ryom-Hansen, S (reprint author), Univ Talca, Inst Matemat & Fis, Talca, Chile.We consider the algebra epsilon(n)(u) introduced by Aicardi and Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for epsilon(n)(u) and show that this is faithful. We use it to give a basis of epsilon(n)(u) and to classify its irreducible representations
We construct a faithful tensor representation for the Yokonuma-Hecke algebra Y r,n , and use it to give a concrete isomorphism between Y r,n and Shoji's modified Ariki-Koike algebra. We give a cellular basis for Y r,n and show that the Jucys-Murphy elements for Y r,n are JM-elements in the abstract sense. Finally, we construct a cellular basis for the Aicardi-Juyumaya algebra of braids and ties.
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 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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