On some properties of the algebra of planar binary trees

Abstract : On some properties of the algebra of planar binary trees. We define an involution which reduces to a block triangular form the Gram matrices of the algebra of planar binary trees. This leads us to conjecture the existence of a tower of algebras admitting the latter as its Grothendieck ring. (C) 2003 Academie des sciences. Publie par Editions scientifiques et medicales Elsevier SAS. Tons droits reserves.