On The Framization Of The Hecke Algebra Of Type B

We give a cross look to two framizations of the Hecke algebra of type B. One of these is a particular case of the cyclotomic Yokonuma–Hecke algebra. The other one was recently introduced by the author, J. Juyumaya and S. Lambropoulou. The purpose of this paper is to show the main concepts and results of both framizations, giving emphasis to the second one, and to provide a preliminary comparison of the invariants constructed from both framizations.