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Lifting to maximal rigid objects in 2-Calabi-Yau triangulated categories

Authors: Yunli Xie and Pin Liu
Journal: Proc. Amer. Math. Soc. 141 (2013), 3361-3367
MSC (2010): Primary 18E30, 16D90
Published electronically: June 17, 2013
MathSciNet review: 3080159
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that a tilting module over the endomorphism algebra of a maximal rigid object in a 2-Calabi-Yau triangulated category lifts to a maximal rigid object in this 2-Calabi-Yau triangulated category. This strengthens recent work of Fu and Liu for cluster-tilting objects.

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Additional Information

Yunli Xie
Affiliation: Department of Mathematics, Sichuan University, 610064 Chengdu, People’s Republic of China–and–Department of Mathematics, Southwest Jiaotong University, 610031 Chengdu, People’s Republic of China

Pin Liu
Affiliation: Department of Mathematics, Southwest Jiaotong University, 610031 Chengdu, People’s Republic of China

Keywords: 2-Calabi-Yau category, tilting modules, maximal rigid objects
Received by editor(s): May 10, 2011
Received by editor(s) in revised form: December 13, 2011
Published electronically: June 17, 2013
Additional Notes: The first author was supported by the NSF of China (Grant 11026190) and the Fundamental Research Funds for the Central Universities (Grants SWJTU11BR098, SWJTU12CX056, and SWJTU12ZT15)
The second author is the corresponding author
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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