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 Grö bner 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.
Original language | English |
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Pages (from-to) | 363-396 |
Number of pages | 34 |
Journal | Duke Mathematical Journal |
Volume | 153 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2010 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics