# The graded structure of Leavitt path algebras

@article{Hazrat2010TheGS, title={The graded structure of Leavitt path algebras}, author={Roozbeh Hazrat}, journal={Israel Journal of Mathematics}, year={2010}, volume={195}, pages={833-895} }

A Leavitt path algebra associates to a directed graph a ℤ-graded algebra and in its simplest form it recovers the Leavitt algebra L(1, k). In this note, we first study this ℤ-grading and characterize the (ℤ-graded) structure of Leavitt path algebras, associated to finite acyclic graphs, Cn-comet, multi-headed graphs and a mixture of these graphs (i.e., polycephaly graphs). The last two types are examples of graphs whose Leavitt path algebras are strongly graded. We give a criterion when a…

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