A Poincaré-Birkhoff-Witt criterion for Koszul operads

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dc.creatorHoffbeck, Eric
dc.date2007-09-14
dc.date2008-11-12
dc.date.accessioned2026-07-07T10:17:18Z
dc.date.available2026-07-07T10:17:18Z
dc.descriptionThe 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.
dc.description24 pages, in english. Changes in v3 : Correction concerning the graded case and some other minor corrections
dc.identifierhttps://arxiv.org/abs/0709.2286
dc.identifierhttp://arxiv.org/abs/0709.2286
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173809
dc.subjectAlgebraic Topology
dc.subject18D50 (55D48); 16S37
dc.titleA Poincaré-Birkhoff-Witt criterion for Koszul operads
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