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arXiv · 1212.0177

Replicating of binary operads, Koszul duality, Manin products and average operators

Jun Pei·Chengming Bai·Li Guo·Xiang Ni
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Abstract

We consider the notions of the replicators, including the duplicator and triplicator, of a binary operad. As in the closely related notions of di-Var-algebra and tri-Var-algebra in [14], they provide a general operadic definition for the recent constructions of replicating the operations of algebraic structures. We show that taking replicators is in Koszul dual to taking successors in [3] for binary quadratic operads and is equivalent to taking the white product with certain operads such as Perm. We also relate the replicators to the actions of average operators.

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Jun Pei, Chengming Bai, Li Guo, Xiang Ni. 2012-12-02. Replicating of binary operads, Koszul duality, Manin products and average operators. https://arxiv.org/abs/1212.0177

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