Work

Gröbner bases for operads

Year: 2010

Type: article

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

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2010-026

Authors: Vladimir Dotsenko, Anton Khoroshkin

Institutions: Dublin Institute For Advanced Studies, Trinity College, Trinity College Dublin, Institute for Theoretical and Experimental Physics

Language: German

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2021827119

FWCI: 5.298

Cites: 25

Cited by: 95

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