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TitleGr\"obner bases for operads.
Author(s) Vladimir Dotsenko, Anton Khoroshkin
TypeArticle in Journal
AbstractWe 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
ISSN0012-7094; 1547-7398/e
URL http://projecteuclid.org/euclid.dmj/1274902083
LanguageEnglish
JournalDuke Math. J.
Volume153
Number2
Pages363--396
PublisherDuke University Press, Durham, NC; University of North Carolina, Chapel Hill, NC
Year2010
Edition0
Translation No
Refereed No
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