Brauer-Thrall Type Theorems for Derived Module Categories

doi:10.1007/s10468-016-9622-7

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	Brauer-Thrall Type Theorems for Derived Module Categories
	Zhang, Chao 1; Han, Yang2
	2016-12-01
发表期刊	ALGEBRAS AND REPRESENTATION THEORY
ISSN	1386-923X
卷号	19 期号:6 页码:1369-1386
摘要	The numerical invariants (global) cohomological length, (global) cohomological width, and (global) cohomological range of a complex (an algebra) are introduced. Cohomological range leads to the concepts of derived bounded algebra and strongly derived unbounded algebra naturally. The first and second Brauer-Thrall type theorems for the bounded derived category of a finite-dimensional algebra over an algebraically closed field are obtained. The first Brauer-Thrall type theorem says that derived bounded algebras are just derived finite algebras. The second Brauer-Thrall type theorem says that an algebra is either derived discrete or strongly derived unbounded, but not both. Moreover, piecewise hereditary algebras and derived discrete algebras are characterized as the algebras of finite global cohomological width and the algebras of finite global cohomological length respectively.
关键词	Derived category Indecomposable object Derived finite algebra Derived discrete algebra Piecewise hereditary algebra
DOI	10.1007/s10468-016-9622-7
语种	英语
资助项目	National Natural Science Foundation of China[11171325] ; National Natural Science Foundation of China[11571341]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000388252300005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24165
专题	系统科学研究所
通讯作者	Han, Yang
作者单位	1.Guizhou Univ, Dept Math, Guiyang 550025, Peoples R China 2.Chinese Acad Sci, KLMM, ISS, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Chao,Han, Yang. Brauer-Thrall Type Theorems for Derived Module Categories[J]. ALGEBRAS AND REPRESENTATION THEORY,2016,19(6):1369-1386.
APA	Zhang, Chao,&Han, Yang.(2016).Brauer-Thrall Type Theorems for Derived Module Categories.ALGEBRAS AND REPRESENTATION THEORY,19(6),1369-1386.
MLA	Zhang, Chao,et al."Brauer-Thrall Type Theorems for Derived Module Categories".ALGEBRAS AND REPRESENTATION THEORY 19.6(2016):1369-1386.