naa a22 4500 510782892 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0138-5 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0138-5 Hazrat R. Department of Pure Mathematics, Queen's University, BT7 1NN, Belfast, UK aut The graded structure of Leavitt path algebras [Elektronische Daten] [R. Hazrat] 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, C n -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 Leavitt path algebra is strongly graded and in particular characterize unital Leavitt path algebras which are strongly graded completely, along the way obtaining classes of algebras which are group rings or crossed-products. In an attempt to generalize the grading, we introduce weighted Leavitt path algebras associated to directed weighted graphs which have natural ⊕ℤ-grading and in their simplest form recover the Leavitt algebras L(n, k). We then show that the basic properties of Leavitt path algebras can be naturally carried over to weighted Leavitt path algebras. Hebrew University Magnes Press, 2013 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 833-895 0021-2172 195:2<833 2013 195 11856 https://doi.org/10.1007/s11856-012-0138-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0138-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hazrat R. Department of Pure Mathematics, Queen's University, BT7 1NN, Belfast, UK aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 833-895 0021-2172 195:2<833 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer