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.
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页码：607 / 650
页数：44
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