Structure theorems for dendriform and tridendriform algebras
Emily BurgunderUniversité Paul Sabatier, Toulouse, France
Bérénice Delcroix-OgerUniversité Paris Diderot, Paris, France
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We state new Cartier–Milnor–Moore Poincaré–Birkhoff–Witt theorems for dendriform and tridendriform structures. We introduce the terplicial coalgebra structure as an analogue in the tridendriform algebras of the duplicial co-structure for the dendriform case, and prove a rigidity theorem.