EAP - Proceedings of the Estonian Academy of Sciences

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proceedings
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On the non-Koszulity of ternary partially associative operad; pp. 355–363

PDF | doi: 10.3176/proc.2010.4.15

Author

Elisabeth Remm

Abstract

We prove that the operad for ternary partially associative algebras is non Koszul. The aim is to underline the problem of computing the dual operad when we consider quadratic operad for n-ary algebras in particular when n is odd. In fact, the dual operad is generally defined in the graded (differential) operad framework. The result of non-Koszulity extends for other operads for (2p + 1)-ary partially associative algebras although the operads for (2p)-ary partially associative algebras are Koszul.

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