Operads of compatible structures and weighted partitions

By H. Strohmayer. 2007

51 citations recorded by the source corpus.

In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large class of algebraic structures by using the poset method of B. Vallette. In particular we show that this is true for the operads of compatible Lie, associative and pre-Lie algebras.

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

View Paper: https://www.semanticscholar.org/paper/61b53f121ac0cfc63f9df85f30b03bae36871655

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Compatible associative products and trees (2008, background): “Koszulness of the operad of two compatible products was proved in [Strohmayer 2008], and this result is crucial for us.”
Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras (2019, background): “On the level of operads, they are also studied as replicators and other compatible structures [22, 27, 36, 37, 40, 41].”
Gröbner bases for operads (2008, result): “The following result was proved in [29] (our original proof in [9] contained a gap).”