On Hilbert series of Koszul operads and a classification result for set-operads

2025/09/17 by Laubie, Paul · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2509.14419

Abstract

Motivated by numerous examples in the literature, we state a conjecture on the Hilbert series of Koszul symmetric operads generated by one element of arity 2. We prove this conjecture for all Koszul symmetric set-operads generated by one element of arity 2 by explicitly classifying those. There are 11 such operads; 4 of them are new.

Citations

• Associator dependent algebras and Koszul duality
• Free product of operads and free basis of Lie-admissible operad
• A Hopf operad of forests of binary trees and related finite-dimensional algebras
• Pre-Lie algebras and the rooted trees operad
• Koszul duality for operads
• Operads, homotopy algebra and iterated integrals for double loop spaces

Cited by

• Homological freeness criterion for operadic modules and application to Cohen-Macalayness of posets

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