Cell structures for the Yokonuma-Hecke algebra and the algebra of braids and ties

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.