从两期大倾斜复合体衍生类别的重元素

IF 0.5 4区数学 Q3 MATHEMATICS Algebras and Representation Theory Pub Date : 2024-02-19 DOI:10.1007/s10468-024-10258-w

Huabo Xu

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引用次数: 0

摘要

我们引入了关联环上大倾斜复数的概念，它是对环上好倾斜模块和倾斜复数的同时概括。给定一个任意关联环上的两期大倾斜复数，我们证明其（派生）内态环的派生模块范畴是给定环的模块范畴和内态环的普遍局部化模块范畴的再互补。这个重归类概括了为投影维数至多为一的好倾斜模建立的重归类。

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Recollements of Derived Categories from Two-Term Big Tilting Complexes

We introduce the notion of big tilting complexes over associative rings, which is a simultaneous generalization of good tilting modules and tilting complexes over rings. Given a two-term big tilting complex over an arbitrary associative ring, we show that the derived module category of its (derived) endomorphism ring is a recollement of the one of the given ring and the one of a universal localization of the endomorphism ring. This recollement generalizes the one established for a good tilting module of projective dimension at most one.

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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.