第二类紧生派生范畴的Koszul对偶性

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2019-09-25 DOI:10.4171/jncg/438

Ai Guan, A. Lazarev

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引用次数: 5

摘要

对于任意dg代数$A$，我们在dg $A$-模上构造了一个闭模型范畴结构，使得相应的同伦范畴是由dg $A$-模紧生成的，这些模在$A$上是有限生成且自由的(不考虑微分)。我们证明了这个封闭模型范畴是Quillen等价于某一可能非共幂的dg协代数上的模范畴，即所谓的a的扩展棒构造。这推广并补充了关联代数的dg - Koszul对偶性的某些方面。

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Koszul duality for compactly generated derived categories of second kind

For any dg algebra $A$ we construct a closed model category structure on dg $A$-modules such that the corresponding homotopy category is compactly generated by dg $A$-modules that are finitely generated and free over $A$ (disregarding the differential). We prove that this closed model category is Quillen equivalent to the category of comodules over a certain, possibly nonconilpotent dg coalgebra, a so-called extended bar construction of $A$. This generalises and complements certain aspects of dg Koszul duality for associative algebras.

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.