Shuffle quadri-algebras and concatenation

  • Mohamed Belhaj Mohamed

    Taibah University, Saudi Arabia, and Université de Sousse, Tunisia
  • Dominique Manchon

    Université Blaise Pascal, Aubière, France
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In this article, we study the shuffle quadri-algebra over some vector space. We prove the existence of some relations between the four quadri-algebra laws which constitute the shuffle product, the concatenation product and the deconcatenation coproduct. We also show that the shuffle quadri-algebra admits two module-algebra structures on itself endowed with the underlying associative algebra structure.