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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Deformed preprojective algebras of generalized Dynkin type


Authors: Jerzy Bialkowski, Karin Erdmann and Andrzej Skowronski
Journal: Trans. Amer. Math. Soc. 359 (2007), 2625-2650
MSC (2000): Primary 16D50, 16E30, 16E40, 16G20, 16G60, 16P10, 18G99
Published electronically: January 25, 2007
MathSciNet review: 2286048
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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 Bialkowski
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
Email: erdmann@maths.ox.ac.uk

Andrzej Skowronski
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Email: skowron@mat.uni.torun.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-07-03948-7
PII: S 0002-9947(07)03948-7
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.