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ISSN 1088-6850(e) ISSN 0002-9947(p)

Deformed preprojective algebras of generalized Dynkin type

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

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