Derived Hall algebras
Derived Hall algebras
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DOI：
10.1215/s0012-7094-06-13536-6
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发表时间：
2005-01
影响因子：
2.5
通讯作者：
B. Toën
中科院分区：
文献类型：
--
作者：
B. Toën
这项工作的目的是定义一个派生的Hall代数$\mathcal{dh}(T)$，它与任何dg-范畴$T$(在一定的有限性条件下)相联系。我们的主要定理是：$\mathcal{dh}(T)$是结合的和单位的。证明了当$T$是交换范畴时，$\mathcal{DH}(T)$包含通常的霍尔代数$\mathcal{H}(T)$.我们还将证明推导出的霍尔数的一个显式公式，它纯粹是关于与$T$相关的三角范畴的不变量。作为一个例子，我们描述了遗传阿贝尔范畴的派生Hall代数。
The purpose of this work is to define a derived Hall algebra $\mathcal{DH}(T)$, associated to any dg-category $T$ (under some finiteness conditions). Our main theorem states that $\mathcal{DH}(T)$ is associative and unital. It is shown that $\mathcal{DH}(T)$ contains the usual Hall algebra $\mathcal{H}(T)$ when $T$ is an abelian category. We will also prove an explicit formula for the derived Hall numbers purely in terms of invariants of the triangulated category associated to $T$. As an example, we describe the derived Hall algebra of an hereditary abelian category.