Abstract
We construct a faithful tensor representation for the Yokonuma–Hecke algebra Yr,n, and use it to give a concrete isomorphism between Yr,n and Shoji's modified Ariki–Koike algebra. We give a cellular basis for Yr,n and show that the Jucys–Murphy elements for Yr,n are JM-elements in the abstract sense. Finally, we construct a cellular basis for the Aicardi–Juyumaya algebra of braids and ties.
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