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Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras


Authors: Manuel Reyes, Daniel Rogalski and James J. Zhang
Journal: Trans. Amer. Math. Soc. 369 (2017), 309-340
MSC (2010): Primary 18E30, 16E35; Secondary 16E65, 16L60, 16S38
DOI: https://doi.org/10.1090/tran/6640
Published electronically: March 18, 2016
MathSciNet review: 3557775
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Abstract: We investigate conditions that are sufficient to make the Ext-algebra of an object in a (triangulated) category into a Frobenius algebra, and compute the corresponding Nakayama automorphism. As an application, we prove the conjecture that $ \textup {hdet}(\mu _A) = 1$ for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra $ A$.


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Additional Information

Manuel Reyes
Affiliation: Department of Mathematics, Bowdoin College, 8600 College Station, Brunswick, Maine 04011-8486
Email: reyes@bowdoin.edu

Daniel Rogalski
Affiliation: Department of Mathematics, University of California San Diego, 9500 Gilman Drive # 0112, La Jolla, California 92093-0112
Email: drogalsk@math.ucsd.edu

James J. Zhang
Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
Email: zhang@math.washington.edu

DOI: https://doi.org/10.1090/tran/6640
Keywords: Skew Calabi-Yau, twisted Calabi-Yau, triangulated category, Frobenius algebra, homological determinant, AS regular algebra.
Received by editor(s): August 18, 2014
Received by editor(s) in revised form: December 23, 2014
Published electronically: March 18, 2016
Additional Notes: This material was based upon work supported by the National Science Foundation under Grant No. 0932078 000, while the authors were in residence at the Mathematical Science Research Institute (MSRI) in Berkeley, California, for the workshop titled “Noncommutative Algebraic Geometry and Representation Theory” during the year of 2013. The authors were also supported by the respective National Science Foundation grants DMS-1407152, DMS-1201572, and DMS-0855743 & DMS-1402863. The first author was supported by an AMS-Simons Travel Grant
Article copyright: © Copyright 2016 American Mathematical Society