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Deformed preprojective algebras of generalized Dynkin type

Authors:	Jerzy Bialkowski Karin Erdmann Andrzej Skowronski

Institution:	Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Torun, Poland ; Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom ; Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Torun, Poland

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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