Replicating of binary operads, Koszul duality, Manin products and average operators
Quantum Algebra
2020-07-27 v2 Combinatorics
Category Theory
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.
Cite
@article{arxiv.1212.0177,
title = {Replicating of binary operads, Koszul duality, Manin products and average operators},
author = {Jun Pei and Chengming Bai and Li Guo and Xiang Ni},
journal= {arXiv preprint arXiv:1212.0177},
year = {2020}
}
Comments
28 pages. 2 figures