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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Deformed preprojective algebras of generalized Dynkin type
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by Jerzy Białkowski, Karin Erdmann and Andrzej Skowroński PDF
Trans. Amer. Math. Soc. 359 (2007), 2625-2650 Request permission

Abstract:

We introduce the class of deformed preprojective algebras of generalized Dynkin graphs $\mathbb {A}_n$ ($n \geq 1$), $\mathbb {D}_n$ ($n \geq 4$), $\mathbb {E}_6$, $\mathbb {E}_7$, $\mathbb {E}_8$ and $\mathbb {L}_n$ ($n \geq 1$) and prove that it coincides with the class of all basic connected finite-dimensional self-injective algebras for which the inverse Nakayama shift $\nu ^{-1} S$ of every non-projective simple module $S$ is isomorphic to its third syzygy $\Omega ^3 S$.
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Additional Information
  • Jerzy Białkowski
  • Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Email: jb@mat.uni.torun.pl
  • Karin Erdmann
  • Affiliation: Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom
  • MR Author ID: 63835
  • ORCID: 0000-0002-6288-0547
  • Email: erdmann@maths.ox.ac.uk
  • Andrzej Skowroński
  • Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Email: skowron@mat.uni.torun.pl
  • Received by editor(s): September 13, 2004
  • Received by editor(s) in revised form: February 15, 2005
  • Published electronically: January 25, 2007
  • Additional Notes: The first and third named authors gratefully acknowledge support from the Polish Scientific Grant KBN No. 1 P03A 018 27
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 2625-2650
  • MSC (2000): Primary 16D50, 16E30, 16E40, 16G20, 16G60, 16P10, 18G99
  • DOI: https://doi.org/10.1090/S0002-9947-07-03948-7
  • MathSciNet review: 2286048