TY - JOUR

T1 - Deformed preprojective algebras of type L

T2 - Külshammer spaces and derived equivalences

AU - Holm, Thorsten

AU - Zimmermann, Alexander

N1 - Funding Information: E-mail addresses: holm@math.uni-hannover.de (T. Holm), alexander.zimmermann@u-picardie.fr (A. Zimmermann). URLs: http://www.iazd.uni-hannover.de/~tholm (T. Holm), http://www.mathinfo.u-picardie.fr/alex/azimengl.html (A. Zimmermann). 1 T.H. is supported by the research grant HO 1880/4-1 of the Deutsche Forschungsgemeinschaft (DFG), in the framework of the Research Priority Program SPP 1388 Representation Theory.

PY - 2011/11/15

Y1 - 2011/11/15

N2 - Białkowski, Erdmann and Skowroński classified those indecomposable selfinjective algebras for which the Nakayama shift of every (non-projective) simple module is isomorphic to its third syzygy. It turned out that these are precisely the deformations, in a suitable sense, of preprojective algebras associated to the simply laced ADE Dynkin diagrams and of another graph Ln, which also occurs in the Happel-Preiser-Ringel classification of subadditive but not additive functions. In this paper we study these deformed preprojective algebras of type Ln via their Külshammer spaces, for which we give precise formulae for their dimensions. These are known to be invariants of the derived module category, and even invariants under stable equivalences of Morita type. As main application of our study of Külshammer spaces we can distinguish many (but not all) deformations of the preprojective algebra of type Ln up to stable equivalence of Morita type, and hence also up to derived equivalence.

AB - Białkowski, Erdmann and Skowroński classified those indecomposable selfinjective algebras for which the Nakayama shift of every (non-projective) simple module is isomorphic to its third syzygy. It turned out that these are precisely the deformations, in a suitable sense, of preprojective algebras associated to the simply laced ADE Dynkin diagrams and of another graph Ln, which also occurs in the Happel-Preiser-Ringel classification of subadditive but not additive functions. In this paper we study these deformed preprojective algebras of type Ln via their Külshammer spaces, for which we give precise formulae for their dimensions. These are known to be invariants of the derived module category, and even invariants under stable equivalences of Morita type. As main application of our study of Külshammer spaces we can distinguish many (but not all) deformations of the preprojective algebra of type Ln up to stable equivalence of Morita type, and hence also up to derived equivalence.

KW - Deformed preprojective algebras

KW - Derived equivalences

KW - Periodic algebras

KW - Primary

KW - Secondary

KW - Stable equivalences of Morita type

KW - Symmetric algebras

UR - http://www.scopus.com/inward/record.url?scp=80053384930&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2011.08.024

DO - 10.1016/j.jalgebra.2011.08.024

M3 - Article

AN - SCOPUS:80053384930

VL - 346

SP - 116

EP - 146

JO - Journal of algebra

JF - Journal of algebra

SN - 0021-8693

IS - 1

ER -