On some anticyclic operads

By Frédéric Chapoton. 2004

51 citations recorded by the source corpus.

oo Lie oo (1) These operads have very nice properties. First of all, they are binary quadratic and Koszul in the sense of the work of Ginzburg and Kapranov on the Koszul duality of operads [7]. More precisely Assoc is self-dual and Lie and Comm are dual to each other. Moreover they are basic examples of cyclic operads, a notion introduced in [5] and related to the moduli spaces of curves with marked points. The developments of Koszul duality of operads and of the theory of cyclic operads were both partly motivated by the work of Kontsevich on noncommutative symplectic geometry [9], where three parallel constructions are made for these three operads. Our aim is to explain that most of the properties of this classical sequence of operads also hold for two other diagrams involving some binary quadratic operads introduced by Loday [11] and others [2, 3]. The first of these diagrams

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4419cc13f9af83d7806ba9403726b570001a9def