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Abstract

Let E be a directed graph, K a field and LK(E) the Leavitt path algebra of E over K. The goal of this paper is to describe the structure of a class of corners of Leavitt path algebras LK(E). The motivation of this work comes from the paper “Corners of Graph Algebras” of Tyrone Crisp in which such corners of graph C*-algebras were investigated completely. Using the same ideas of Tyrone Crisp, we will show that for any finite subset X of vertices in a directed graph E such that the hereditary subset HE(X) generated by X is finite, the corner ( ) ( )( )     K v X v X v L E v is isomorphic to the Leavitt path algebra LK(EX) of some graph EX. We also provide a way how to construct this graph EX.



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Issue: Vol 2 No 4 (2018)
Page No.: 75-81
Published: Aug 13, 2019
Section: Original Research
DOI: https://doi.org/10.32508/stdjns.v2i4.813

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Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Trinh, D. (2019). A class of corners of a Leavitt path algebra. Science and Technology Development Journal - Natural Sciences, 2(4), 75-81. https://doi.org/https://doi.org/10.32508/stdjns.v2i4.813

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