The Koszul Complex is the Cotangent Complex

被引：12

作者：

Milles, Joan ^{[1
]}

机构：

[1] Univ Nice, Lab JA Dieudonne, F-06108 Nice 02, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2012年 / 2012卷 / 03期

关键词：

DUALITY; ALGEBRAS; COHOMOLOGY;

D O I：

10.1093/imrn/rnr034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend the Koszul duality theory of associative algebras to algebras over an operad. Recall that in the classical case, this Koszul duality theory relies on an important chain complex: the Koszul complex. We show that the cotangent complex, involved in the cohomology theory of algebras over an operad, plays the role of the Koszul complex.

引用

页码：607 / 650

页数：44

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