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Finite-dimensional representations of Leavitt path algebras

Authors
  • Koç, Ayten
  • Özaydın, Murad
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
Dec 13, 2017
Volume
30
Issue
4
Pages
915–928
Identifiers
DOI: 10.1515/forum-2016-0268
Source
De Gruyter
Keywords
License
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Abstract

When Γ is a row-finite digraph, we classify all finite-dimensional modules of the Leavitt path algebra L ⁢ ( Γ ) {L(\Gamma)} via an explicit Morita equivalence given by an effective combinatorial (reduction) algorithm on the digraph Γ. The category of (unital) L ⁢ ( Γ ) {L(\Gamma)} -modules is equivalent to a full subcategory of quiver representations of Γ. However, the category of finite-dimensional representations of L ⁢ ( Γ ) {L(\Gamma)} is tame in contrast to the finite-dimensional quiver representations of Γ, which are almost always wild.

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