Gr\"obner bases for operads
Quantum Algebra
2019-12-19 v2
Abstract
We define a new monoidal category on collections (shuffle composition). Monoids in this category (shuffle operads) turn out to bring a new insight in the theory of symmetric operads. For this category, we develop the machinery of Gr\"obner bases for operads, and present operadic versions of Bergman's Diamond Lemma and Buchberger's algorithm. This machinery can be applied to study symmetric operads. In particular, we obtain an effective algorithmic version of Hoffbeck's PBW criterion of Koszulness for (symmetric) quadratic operads.
Cite
@article{arxiv.0812.4069,
title = {Gr\"obner bases for operads},
author = {Vladimir Dotsenko and Anton Khoroshkin},
journal= {arXiv preprint arXiv:0812.4069},
year = {2019}
}
Comments
28 pages, to appear in Duke Math. Journal