On the non-Koszulity of ternary partially associative operad

Proceedings of the Estonian Academy of Sciences

Elisabeth Remm¹ 

[1] $$

关键词: n-ary algebras;    operads;    partial/total associativity;    degree d generating operation;    Koszulity;   

DOI  :  10.3176/proc.2010.4.15

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

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.

【 授权许可】

Unknown