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Module varieties and representation type of finite-dimensional algebras
Journal article   Peer reviewed

Module varieties and representation type of finite-dimensional algebras

Calin Chindris, Ryan Kinser and Jerzy Weyman
International mathematics research notices, Vol.2015(3), pp.631-650
01/30/2012
DOI: 10.1093/imrn/rnt216
url
https://arxiv.org/pdf/1201.6422View
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Abstract

Int. Math. Res. Notices (2015) 2015 (3): 631-650 In this paper we seek geometric and invariant-theoretic characterizations of (Schur-)representation finite algebras. To this end, we introduce two classes of finite-dimensional algebras: those with the dense-orbit property and those with the multiplicity-free property. We show first that when a connected algebra A admits a preprojective component, each of these properties is equivalent to A being representation-finite. Next, we give an example of an algebra which is not representation-finite but still has the dense-orbit property. We also show that the string algebras with the dense orbit-property are precisely the representation-finite ones. Finally, we show that a tame algebra has the multiplicity-free property if and only if it is Schur-representation-finite.
Mathematics - Representation Theory

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