Mathematics – Rings and Algebras
Scientific paper
2010-05-11
Mathematics
Rings and Algebras
32 pages, (even more) polishing
Scientific paper
Leavitt path algebras associate to directed graphs a $\mathbb Z$-graded algebra and in their simplest form recover the Leavitt algebras $L(1,k)$. In this note, we first study this $\mathbb Z$-grading and characterize the ($\mathbb Z$-graded) structure of Leavitt path algebras, associated to finite acyclic graphs, $C_n$-comet and multi-headed graphs. The last two type are examples of graphs whose Leavitt path algebras are strongly graded. We characterize Leavitt path algebras which are strongly graded, 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 $\textstyle{\bigoplus} \mathbb Z$-grading and in their simplest form recover the Leavitt algebras $L(n,k)$. We then establish some basic properties of these algebras.
No associations
LandOfFree
The graded structure of Leavitt Path algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The graded structure of Leavitt Path algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The graded structure of Leavitt Path algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-385622