On the Nonkoszulity of (2p + 1)-ary Partially Associative Operads Adress : Lmia. Uha 4 Rue Des Frèreslumì Ere F. 68093 Mulhouse Cedex

We want to present here the part of the work in common with Martin Markl [11] which concerns quadratic operads for n-ary algebras and their dual for n odd. We will focus on the ternary case (i.e n = 3). The aim is to underline the problem of computing the dual operad and the fact that this last is in general defined in the graded differential operad framework. We prove that the operad associated to (2p+ 1)-ary partially associative algebra is not Koszul. Recall that, in the even case, this operad is Koszul.