Interaction between Representation Theory of Algebras and Cluster Theory
代数表示论与簇论的相互作用
基本信息
- 批准号:RGPIN-2018-06107
- 负责人:
- 金额:$ 1.68万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2020
- 资助国家:加拿大
- 起止时间:2020-01-01 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Our objective is to study the representation theory of artin algebras with connection to cluster theory. Our methodology consists of AR-theory, tilting theory and covering theory.
1) For artin algebras, we shall describe the shapes of some special AR-components; classify representation-finite algebras whose radical has a small nilpotency; characterize the representation-finiteness in terms of their AR-quievrs; construct all preprojective or preinjective tilting modules over a hereditary algebra and characterize cluster tilted algebras. For a string bound quiver with infinite nonzero paths or a species of an infinite Dynkin valued quiver, we shall classify the indecomposable representations and describe their AR-components.
2) Working with extension closed subcategories of triangulated categories, we shall unify the AR-theory studied independently in module categories over rings, exact categories, abelian categories and triangulated categories. This will yield existence theorems of almost split sequences in the representation category of a bound quiver with infinite non-zero paths and that of species of infinite valued quivers with no infinite path.
3) We shall provide some new points of view to study the homological properties of algebras. We shall attack No Loop Conjecture from the AR-quiver of the derived category of artin algebras of finite global dimension and establish Finitistic Dimension Conjecture for algebras with a finite singularity category. We shall find a criterion for an oriented cycle in the quiver of an elementary algebra to support a semisimple module of infinite projective dimension. We shall establish No Loop Conjecture for artin algebras with radical cubed zero and Extension Conjecture for elementary algebras with radical cubed zero.
4) We shall construct a Galois covering for the derived category of a quadratic monomial algebra in order to classify the indecomposable complexes and describe their AR-components in the string case. We shall study a new category, that is the Verdier quotient of the derived category of finitely presented representations of a strongly locally finite quiver by the triangulated subcategory of finite dimensional representations.
5) We shall show that the canonical orbit category of the derived category of the representation category of a species of a finite valued quiver is a cluster category, and it categorifies the corresponding cluster algebra. We shall construct cluster categories of types B infinity and C infinity.
6) Given a cluster category of type A infinity or A double infinity, we shall be interested in a criterion for a rigid subcategory to be maximal rigid and in a method to construct all the cluster tilting subcategories.
7) Given a cluster category, we shall characterize its rank in terms of some of its intrinsic properties and show that it is the classical cluster category associated with a Dynkin quiver if it is of finite type.
我们的目标是研究与聚类理论有联系的代数的表示理论。我们的方法包括ar理论、倾斜理论和覆盖理论。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Liu, Shiping其他文献
Role of endoplasmic reticulum autophagy in acute lung injury.
- DOI:
10.3389/fimmu.2023.1152336 - 发表时间:
2023 - 期刊:
- 影响因子:7.3
- 作者:
Liu, Shiping;Fang, Xiaoyu;Zhu, Ruiyao;Zhang, Jing;Wang, Huijuan;Lei, Jiaxi;Wang, Chaoqun;Wang, Lu;Zhan, Liying - 通讯作者:
Zhan, Liying
High Throughput Single Cell RNA Sequencing, Bioinformatics Analysis and Applications
- DOI:
10.1007/978-981-13-0502-3_4 - 发表时间:
2018-01-01 - 期刊:
- 影响因子:0
- 作者:
Huang, Xiaoyun;Liu, Shiping;Hou, Yong - 通讯作者:
Hou, Yong
20-Hydroxyecdysone-responsive microRNAs of insects
- DOI:
10.1080/15476286.2020.1775395 - 发表时间:
2020-06-15 - 期刊:
- 影响因子:4.1
- 作者:
Jin, Xiaoli;Wu, Xiaoyan;Liu, Shiping - 通讯作者:
Liu, Shiping
Spectral distances on graphs
- DOI:
10.1016/j.dam.2015.04.011 - 发表时间:
2015-08-20 - 期刊:
- 影响因子:1.1
- 作者:
Gu, Jiao;Hua, Bobo;Liu, Shiping - 通讯作者:
Liu, Shiping
Effects of different water levels on cotton growth and water use through drip irrigation in an arid region with saline ground water of Northwest China
- DOI:
10.1016/j.agwat.2012.02.013 - 发表时间:
2012-06-01 - 期刊:
- 影响因子:6.7
- 作者:
Kang, Yaohu;Wang, Ruoshui;Liu, Shiping - 通讯作者:
Liu, Shiping
Liu, Shiping的其他文献
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{{ truncateString('Liu, Shiping', 18)}}的其他基金
Interaction between Representation Theory of Algebras and Cluster Theory
代数表示论与簇论的相互作用
- 批准号:
RGPIN-2018-06107 - 财政年份:2022
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Interaction between Representation Theory of Algebras and Cluster Theory
代数表示论与簇论的相互作用
- 批准号:
RGPIN-2018-06107 - 财政年份:2021
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Interaction between Representation Theory of Algebras and Cluster Theory
代数表示论与簇论的相互作用
- 批准号:
RGPIN-2018-06107 - 财政年份:2019
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Interaction between Representation Theory of Algebras and Cluster Theory
代数表示论与簇论的相互作用
- 批准号:
RGPIN-2018-06107 - 财政年份:2018
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Representation theory of algebras and related topics
代数表示论及相关主题
- 批准号:
172797-2013 - 财政年份:2017
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Representation theory of algebras and related topics
代数表示论及相关主题
- 批准号:
172797-2013 - 财政年份:2016
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Representation theory of algebras and related topics
代数表示论及相关主题
- 批准号:
172797-2013 - 财政年份:2015
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Representation theory of algebras and related topics
代数表示论及相关主题
- 批准号:
172797-2013 - 财政年份:2014
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Representation theory of algebras and related topics
代数表示论及相关主题
- 批准号:
172797-2013 - 财政年份:2013
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Representations of Artin algebras
Artin 代数的表示
- 批准号:
172797-2008 - 财政年份:2012
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
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