In this paper we represent the classical braids in the classical and the
adelic Yokonuma-Hecke algebras. More precisely, we define the completion of the
framed braid group and we introduce the adelic Yokonuma-Hecke algebras, in
analogy to the notions of p-adic framed braids and p-adic Yokonuma-Hecke
algebras introduced in \cite{jula,jula2}. We further construct an adelic Markov
trace, analogous to a p-adic Markov trace constructed in \cite{jula2}. Using
the traces in \cite{ju} and the adelic Markov trace we define topological
invariants of classical knots and links, upon imposing some condition (in
analogy to the invariants of framed links defined in \cite{jula2}). These
invariants are related to a cubic skein relation coming from the Yokonuma-Hecke
algebra.