On derived equivalences and homological dimensions

doi:10.1515/crelle-2020-0006

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	On derived equivalences and homological dimensions
	Fang, Ming 1,2; Hu, Wei 3; Koenig, Steffen 4
	2021
发表期刊	JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
ISSN	0075-4102
卷号	770 页码:59-85
摘要	Unlike Hochschild (co)homology and K-theory, global and dominant dimensions of algebras are far from being invariant under derived equivalences in general. We show that, however, global dimension and dominant dimension are derived invariant when restricting to a class of algebras with anti-automorphisms preserving simples. Such anti-automorphisms exist for all cellular algebras and in particular for many finite-dimensional algebras arising in algebraic Lie theory. Both dimensions then can be characterised intrinsically inside certain derived categories. On the way, a restriction theorem is proved, and used, which says that derived equivalences between algebras with positive nu-dominant dimension always restrict to derived equivalences between their associated self-injective algebras, which under this assumption do exist.
DOI	10.1515/crelle-2020-0006
收录类别	SCI
语种	英语
资助项目	NSFC[11471315] ; NSFC[11321101] ; NSFC[11331006] ; NSFC[11471038] ; NSFC[11688101] ; Fundamental Research Funds for the Central Universities
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000604917600003
出版者	WALTER DE GRUYTER GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57950
专题	中国科学院数学与系统科学研究院
通讯作者	Fang, Ming
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, HLM, HCMS, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China 4.Univ Stuttgart, Inst Algebra & Number Theory, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
推荐引用方式 GB/T 7714	Fang, Ming,Hu, Wei,Koenig, Steffen. On derived equivalences and homological dimensions[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK,2021,770:59-85.
APA	Fang, Ming,Hu, Wei,&Koenig, Steffen.(2021).On derived equivalences and homological dimensions.JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK,770,59-85.
MLA	Fang, Ming,et al."On derived equivalences and homological dimensions".JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK 770(2021):59-85.