Vol. 289, No. 2, 2017

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Cluster tilting modules and noncommutative projective schemes

Kenta Ueyama

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

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.

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
Received: 13 April 2016
Revised: 6 February 2017
Accepted: 10 February 2017
Published: 19 June 2017
Kenta Ueyama
Department of Mathematics
Faculty of Education
Hirosaki University
1 Bunkyocho, Hirosaki
Aomori 036-8560