Modified Ringel–Hall algebras, Green’s formula andderived Hall algebras
Modified Ringel–Hall algebras, Green’s formula andderived Hall algebras
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修正的林格尔霍尔代数、格林公式和导出的霍尔代数
DOI：
10.1016/j.jalgebra.2019.02.009
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发表时间：
2019
影响因子：
0.9
通讯作者：
彭联刚
中科院分区：
文献类型：
--
作者：
林记;彭联刚
本文从有界z级复形的范畴C b (A)出发，定义了遗传阿贝尔范畴A的修正Ringel-Hall代数M H (A)。得到了两个主要结果。一是利用改进的Ringel-Hall代数的关联乘法，给出格林公式在Ringel-Hall数上的一个新的证明。二是证明了在某些扭曲情况下，导出的霍尔代数可以嵌入到修正的林格尔-霍尔代数中。作为第二个结果的结果，我们得到了在某些扭曲情况下，修正的林格尔-霍尔代数与派生的霍尔代数的张量代数和无环复形的环面是同构的，因此修正的林格尔-霍尔代数在派生等价下是不变的。
In this paper we define the modified Ringel–Hall algebra M H (A) of a hereditary abelian category A from the category C b (A) of bounded Z-graded complexes. Two main results are obtained. One is to give a new proof of Green's formula on Ringel–Hall numbers by using the associative multiplication of the modified Ringel–Hall algebra. The other is to show that in certain twisted cases the derived Hall algebra can be embedded in the modified Ringel–Hall algebra. As a consequence of the second result, we get that in certain twisted cases the modified Ringel–Hall algebra is isomorphic to the tensor algebra of the derived Hall algebra and the torus of acyclic complexes and therefore the modified Ringel–Hall algebra is invariant under derived equivalences.