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In this article we study the packed words Hopf algebra WMat introduced byDuchamp, Hoang-Nghia et Tanasa. We start by explaining that WMat is not cofree,giving its antipode and describing its graded dual. We consider then a Hopfsub-algebra of permutations called $\mathfrak{S}\mathcal{H}$. Its graded dual$\mathfrak{S}\mathcal{H}^\circledast$ has a quadri-algebra structure, so it hasa double dendriform algebra structure too. Thereafter, we introduce ISPW, aHopf algebra of increasing strict packed words. It is graded, connected andcocommutative so is isomorphic to the enveloping algebra of its primitiveelements. We describe some families of primitive elements. We prove that ISPWand non commutative symmetric functions are isomorphic. We define then anextended compositions Hopf algebra $\mathcal{C}_e$. It is not cocommutative butits primitive elements and those from ISPW are linked. We give aninterpretation of $\mathcal{C}_e$ in terms of a semi-direct coproduct Hopfalgebra. By using this, we can define two actions groups. We finish by givingan explicit isomorphism between ISPW$^\circledast$ and QSym and another onebetween ISPW and NSym.

A propos de l'alg\`ebre de Hopf des mots tass\'es WMat