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arXiv · 1607.04622

Finite Dimensional Representations of Leavitt Path Algebras

Ayten Koç·Murad Özaydın
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Abstract

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

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BibTeXRIS

Ayten Koç, Murad Özaydın. 2016-07-15. Finite Dimensional Representations of Leavitt Path Algebras. https://arxiv.org/abs/1607.04622

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