Transactions of the American Mathematical Society

Author(s): Jerzy Bialkowski; Karin Erdmann; Andrzej Skowronski
Journal: Trans. Amer. Math. Soc. 359 (2007), 2625-2650.
MSC (2000): Primary 16D50, 16E30, 16E40, 16G20, 16G60, 16P10, 18G99
Posted: January 25, 2007
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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

is isomorphic to its third syzygy $\Omega^3 S$ .

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

DOI: 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
Posted: 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 of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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