从格林公式到派生的霍尔代数

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-05-17 DOI:10.1007/s10468-025-10335-8

Ji Lin

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引用次数: 0

摘要

本文的目的是阐明格林公式与推导出的霍尔代数的乘法结合律在Toën （Duke Math J 135(3):587- 615,2006）、Xiao and Xu （Duke Math J 143(2):357-373, 2008）和Xu and Chen （Algebr representation Theory 16(3):673-687, 2013）意义上的关系。设\(\mathcal {A}\)为有限遗传阿贝尔范畴。已知推导出的霍尔代数\(\mathcal {D}\mathcal {H}_t(\mathcal {A})\)的结合律隐含格林公式。我们引入了一个新的代数\({\mathcal {L}}_t({\mathcal {A}})\)，它的结合律由格林公式推导而来，并证明了它与推导出来的霍尔代数\(\mathcal {D}\mathcal {H}_t(\mathcal {A})\)是同构的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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From Green’s Formula to Derived Hall Algebras

The aim of this note is to clarify the relationship between Green’s formula and the associativity of multiplication for derived Hall algebra in the sense of Toën (Duke Math J 135(3):587-615, 2006), Xiao and Xu (Duke Math J 143(2):357-373, 2008) and Xu and Chen (Algebr Represent Theory 16(3):673-687, 2013). Let \(\mathcal {A}\) be a finitary hereditary abelian category. It is known that the associativity of the derived Hall algebra \(\mathcal {D}\mathcal {H}_t(\mathcal {A})\) implies Green’s formula. We introduce a new algebra \({\mathcal {L}}_t({\mathcal {A}})\) whose associativity is deduced from Green’s formula, and show that it is isomorphic to the derived Hall algebra \(\mathcal {D}\mathcal {H}_t(\mathcal {A})\).

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.