An Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras

We first present an Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras $widehat{Y}_{r,n}(q)$ to give a new proof of the fact, which was previously proved by Chlouveraki and Secherre, that $widehat{Y}_{r,n}(q)$ is a particular case of the pro-$p$-Iwahori-Hecke algebras defined by Vigneras, meanwhile, we give one application. Using the new presentation, we then give a third presentation of $widehat{Y}_{r,n}(q),$ from which we immediately get an unexpected result, that is, the extended affine Hecke algebra of type $A$ is a subalgebra of the affine Yokonuma-Hecke algebra.