Dotsenko, Vladimir; Markl, Martin; Remm, Elisabeth

Non-Koszulness of Operads and Positivity of Poincaré Series

Doc. Math. 25, 309-328 (2020)
DOI: 10.25537/dm.2020v25.309-328

Summary

We prove that the operad of mock partially associative \(n\)-ary algebras is not Koszul, as conjectured by the second and the third author in 2009, and utilise the Zeilberger's algorithm for hypergeometric summation to demonstrate that non-Koszulness of that operad for \(n=8\) cannot be established by hunting for negative coefficients in the inverse of its Poincaré series.

Mathematics Subject Classification

18M70, 13D40, 33E30, 33F10, 39A06, 39A22

Keywords/Phrases

operad, Koszul duality, Koszulness, Zeilberger's algorithm

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Affiliation

Dotsenko, Vladimir
IRMA, UMR 7501, Université de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg Cedex, France
Markl, Martin
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, and MFF UK, Sokolovská 83, 186 75 Prague 8, Czech Republic
Remm, Elisabeth
IRIMAS, EA 7499, Université de Haute Alsace, 4, rue des Frères Lumière, 68093 Mulhouse Cedex, France

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