Noncommutative quasi-resolutions

JOURNAL OF ALGEBRA

卷:536

Article

Qin, X-S¹  Wang, Y-H²  Zhang, J. J.³ 

[1] Fudan Univ, Shanghai Ctr Math Sci, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Shanghai Univ Finance & Econ, Sch Math, Shanghai Key Lab Financial Informat Technol, Shanghai 200433, Peoples R China

[3] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

关键词: Noncommutative crepant resolution (NCCR);    Noncommutative quasi-resolution (NQR);    Morita equivalent;    Derived equivalent;    Auslander-Gorenstein algebra;    Auslander regular algebra;    Cohen-Macaulay algebra;    Dimension function;   

DOI  :  10.1016/j.jalgebra.2019.07.015

来源: Elsevier

【 摘 要 】

The notion of a noncommutative quasi-resolution is introduced for a noncommutative noetherian algebra with singularities, even for a non-Cohen-Macaulay algebra. If A is a commutative normal Gorenstein domain, then a noncommutative quasi-resolution of A naturally produces a noncommutative crepant resolution (NCCR) of A in the sense of Van den Bergh, and vice versa. Under some mild hypotheses, we prove that (i) in dimension two, all noncommutative quasi-resolutions of a given noncommutative algebra are Morita equivalent, and (ii) in dimension three, all noncommutative quasi-resolutions of a given noncommutative algebra are derived equivalent. These assertions generalize important results of Van den Bergh, Iyama-Reiten and Iyama-Wemyss in the commutative and central-finite cases. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free