On derived equivalences and homological dimensions
文献类型：期刊论文
| 作者 | Fang, Ming1,2; Hu, Wei3; Koenig, Steffen4 |
| 刊名 | JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
 |
| 出版日期 | 2021 |
| 卷号 | 770页码:59-85 |
| ISSN号 | 0075-4102 |
| DOI | 10.1515/crelle-2020-0006 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000604917600003 |
| 出版者 | WALTER DE GRUYTER GMBH |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/57949]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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