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 $\Omega ^3 S$.References
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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