Gröbner bases for operads

Dotsenko, Vladimir and Khoroshkin, Anton (2009) Gröbner bases for operads. Duke Mathematical Journal, 153 (2). pp. 363-396. ISSN 0012-7094

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Official URL: http://doi.org/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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:19
Last Modified: 26 Jul 2018 09:59
URI: http://dair.dias.ie/id/eprint/247

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