J. Leray
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引用次数: 6

摘要

本文构造了原操作数的bar-cobar共轭和Koszul对偶理论,原操作数是一种操作类型概念,忠实地编码对角对称双代数的某些范畴,如双李代数(DLie)。给出了二元二次元算子是Koszul的判据,并将其成功地应用于二元二次元算子的DLie。作为推论,我们推导出编码双泊松代数的合适DPois是Koszul。这允许我们描述在非交换几何中起关键作用的双泊松代数的同伦性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Protoperads II: Koszul duality
In this paper, we construct a bar-cobar adjunction and a Koszul duality theory for protoperads, which are an operadic type notion encoding faithfully some categories of bialgebras with diagonal symmetries, like double Lie algebras (DLie). We give a criterion to show that a binary quadratic protoperad is Koszul and we apply it successfully to the protoperad DLie. As a corollary, we deduce that the properad DPois which encodes double Poisson algebras is Koszul. This allows us to describe the homotopy properties of double Poisson algebras which play a key role in non commutative geometry.
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