A Poincaré–Birkhoff–Witt criterion for Koszul operads

By Eric Hoffbeck. 2007

110 citations recorded by the source corpus.

The aim of this article is to give a criterion, generalizing the criterion introduced by Priddy for algebras, to prove that an operad is Koszul. We define the notion of Poincaré–Birkhoff–Witt basis in the context of operads. Then we show that an operad having a Poincaré–Birkhoff–Witt basis is Koszul. Besides, we obtain that the Koszul dual operad has also a Poincaré–Birkhoff–Witt basis. We check that the classical examples of Koszul operads (commutative, associative, Lie, Poisson) have a Poincaré–Birkhoff–Witt basis. We also prove by our methods that new operads are Koszul.

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

View Paper: https://www.semanticscholar.org/paper/bab15c05cc70e90f4ce0eb71e33a594d8172fecb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On quadri-algebras (2014, methodology): “Let us give here a second proof, with the help of the rewriting method of [9, 2, 12].”