A Poincaré-Birkhoff-Witt criterion for Koszul operads

Details A Poincaré-Birkhoff-Witt criterion for Koszul operads A Poincaré-Birkhoff-Witt criterion for Koszul operads

2007-09-14

arxiv.org/abs/0709.2286v3

Mathematics

Algebraic Topology

24 pages, in english. Changes in v3 : Correction concerning the graded case and some other minor corrections

Scientific paper

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

Affiliated with

Also associated with

No associations

Rating

A Poincaré-Birkhoff-Witt criterion for Koszul operads does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Poincaré-Birkhoff-Witt criterion for Koszul operads, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Poincaré-Birkhoff-Witt criterion for Koszul operads will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-616437