Gröbner bases for operads

Vladimir Dotsenko, Anton Khoroshkin

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)363-396
Number of pages34
JournalDuke Mathematical Journal
Issue number2
StatePublished - Jun 2010
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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