Gröbner bases for operads

Details Gröbner bases for operads Gröbner bases for operads

2008-12-21

arxiv.org/abs/0812.4069v2

Duke Math. J. Volume 153, Number 2 (2010), 363-396

Mathematics

Quantum Algebra

28 pages, to appear in Duke Math. Journal

Scientific paper

10.1215/00127094-2010-026

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.

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