Gröbner bases for operads
arXiv:0812.4069 · doi:10.1215/00127094-2010-026
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 Gröbner 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.
28 pages, to appear in Duke Math. Journal
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Cited by in corpus (38)
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