A Poincar,-Birkhoff-Witt criterion for Koszul operads

作者：Hoffbeck Eric^*

来源：Manuscripta Mathematica, 2010, 131(1-2): 87-110.

DOI：10.1007/s00229-009-0303-2

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 Poincar,-Birkhoff-Witt basis in the context of operads. Then we show that an operad having a Poincar,-Birkhoff-Witt basis is Koszul. Besides, we obtain that the Koszul dual operad has also a Poincar,-Birkhoff-Witt basis. We check that the classical examples of Koszul operads (commutative, associative, Lie, Poisson) have a Poincar,-Birkhoff-Witt basis. We also prove by our methods that new operads are Koszul.

• 出版日期2010-1