Vol. 289, No. 2, 2017

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Cluster tilting modules and noncommutative projective schemes

Kenta Ueyama

Vol. 289 (2017), No. 2, 449–468
DOI: 10.2140/pjm.2017.289.449
Abstract

We study the relationship between equivalences of noncommutative projective schemes and cluster tilting modules. In particular, we prove the following result. Let A be an AS-Gorenstein algebra of dimension d 2 and tailsA the noncommutative projective scheme associated to A. If gldim(tailsA) < and A has a (d1)-cluster tilting module X with the property that its graded endomorphism algebra is -graded, then the graded endomorphism algebra B of a basic (d1)-cluster tilting submodule of X is a two-sided noetherian -graded AS-regular algebra over B0 of global dimension d such that tailsB is equivalent to tailsA.

Keywords
noncommutative projective scheme, cluster tilting module, AS-Gorenstein algebra, AS-regular algebra, ASF-regular algebra
Mathematical Subject Classification 2010
Primary: 16S38
Secondary: 14A22, 16G50, 16W50
Milestones
Received: 13 April 2016
Revised: 6 February 2017
Accepted: 10 February 2017
Published: 19 June 2017
Authors
Kenta Ueyama
Department of Mathematics
Faculty of Education
Hirosaki University
1 Bunkyocho, Hirosaki
Aomori 036-8560
Japan