On the NonKoszulity of (2p+1)-ary partially associative Operads

Details On the NonKoszulity of (2p+1)-ary partially associative Operads On the NonKoszulity of (2p+1)-ary partially associative Operads

2008-12-14

arxiv.org/abs/0812.2687v1

Mathematics

Algebraic Topology

Talk given in the 4th Baltic-Nordic Workshop, Tartu, october 2008

Scientific paper

We present a study of 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 3-ary partially associative algebra is not Koszul. Recall that, if n is even, the operad of n-ary partially associative algebras is Koszul.

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