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arXiv 0709.22862007-09math.AT

Koszul算子的Poincaré-Birkhoff-Witt判据

A Poincaré-Birkhoff-Witt criterion for Koszul operads

Eric Hoffbeck

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

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摘要：

本文的目的是给出一个判定算子是Koszul的判据，推广了Priddy为代数引入的判据。我们定义的概念的庞加莱-伯克霍夫-维特基础的背景下，操作。然后，我们表明，一个操作有一个庞加莱-伯克霍夫-维特基是Koszul。此外，我们还得到了Koszul对偶算子也有Poincare-Birkhoff-Witt基.我们检查，经典的例子Koszul操作（交换，联想，李）有一个庞加莱-伯克霍夫-维特的基础。

英文摘要：

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.

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