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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras
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by Manuel Reyes, Daniel Rogalski and James J. Zhang PDF
Trans. Amer. Math. Soc. 369 (2017), 309-340 Request permission

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 $\mathrm {hdet}(\mu _A) = 1$ 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
  • MR Author ID: 835471
  • ORCID: 0000-0002-5068-7205
  • Email: reyes@bowdoin.edu
  • Daniel Rogalski
  • Affiliation: Department of Mathematics, University of California San Diego, 9500 Gilman Drive # 0112, La Jolla, California 92093-0112
  • MR Author ID: 734142
  • Email: drogalsk@math.ucsd.edu
  • James J. Zhang
  • Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
  • MR Author ID: 314509
  • Email: zhang@math.washington.edu
  • 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
  • © Copyright 2016 American Mathematical Society
  • 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
  • MathSciNet review: 3557775