Shuffle quadri-algebra and concatenation

Abstract

In this article, we study the shuffle quadri-algebra H. We prove the existence of some relations between quadri-algebra laws which constitute shuffle product, the concatenation product and the deconcatenation coproduct. We also show that the underlying shuffle algebra has two module-algebra structures on itself.

23 pages. Revised version, to appear in the proceedings of the CARMA conference, Luminy, June 26-30th 2017