1 June 2010 Gröbner bases for operads
Vladimir Dotsenko, Anton Khoroshkin
Author Affiliations +
Duke Math. J. 153(2): 363-396 (1 June 2010). DOI: 10.1215/00127094-2010-026

Abstract

We define a new monoidal structure on the category of 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 Poincaré-Birkhoff-Witt criterion of Koszulness for (symmetric) quadratic operads

Citation

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Vladimir Dotsenko. Anton Khoroshkin. "Gröbner bases for operads." Duke Math. J. 153 (2) 363 - 396, 1 June 2010. https://doi.org/10.1215/00127094-2010-026

Information

Published: 1 June 2010
First available in Project Euclid: 26 May 2010

zbMATH: 0895.16020
MathSciNet: MR2667136
Digital Object Identifier: 10.1215/00127094-2010-026

Subjects:
Primary: 22E50 , 46F10
Secondary: 14L24 , 14L30 , 20C99 , 20G05 , 22E45

Rights: Copyright © 2010 Duke University Press

Vol.153 • No. 2 • 1 June 2010
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