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}
}
  • R. Hazrat
  • Published 11 May 2010
  • Mathematics
  • Israel Journal of Mathematics
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… 

The graded structure of algebraic Cuntz-Pimsner rings

The graded Grothendieck group and the classification of Leavitt path algebras

  • R. Hazrat
  • Mathematics
    Mathematische Annalen
  • 2012
This paper is an attempt to show that, parallel to Elliott’s classification of AF C*-algebras by means of K-theory, the graded K0-group classifies Leavitt path algebras completely. In this direction,

Connections between Abelian sandpile models and the $K$-theory of weighted Leavitt path algebras

. In our main result, we establish that any conical sandpile monoid M = SP( E ) of a directed sandpile graph E can be realised as the V -monoid of a weighted Leavitt path algebra L k ( F, w ) (where

Leavitt Path Algebras of Hypergraphs

  • Raimund Preusser
  • Mathematics
    Bulletin of the Brazilian Mathematical Society, New Series
  • 2019
We define Leavitt path algebras of hypergraphs generalizing simultaneously Leavitt path algebras of separated graphs and Leavitt path algebras of vertex-weighted graphs (i.e. weighted graphs that

The V-monoid of a weighted Leavitt path algebra

We compute the V-monoid of a weighted Leavitt path algebra of a rowfinite weighted graph, correcting a wrong computation of the V-monoid that exists in the literature. Further we show that the

Epsilon-strongly graded Leavitt path algebras

Given a directed graph $E$ and a unital ring $R$ one can define the Leavitt path algebra with coefficients in $R$, denoted by $L_R(E)$. For an arbitrary group $G$, $L_R(E)$ can be viewed as a

Properties of the gradings on ultragraph algebras via the underlying combinatorics

There are two established gradings on Leavitt path algebras associated with ultragraphs, namely the grading by the integers group and the grading by the free group on the edges. In this paper, we

Algebraic entropy and a complete classification of path algebras over finite graphs by growth

. The Gelfand-Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce the algebraic entropy for path algebras. For the
...

References

SHOWING 1-10 OF 26 REFERENCES

K-Theory of Azumaya Algebras

For an Azumaya algebra $A$ which is free over its centre $R$, we prove that the $K$-theory of $A$ is isomorphic to $K$-theory of $R$ up to its rank torsion. We observe that a graded central simple

A first course in noncommutative rings

This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the

Locally finite Leavitt path algebras

A group-graded K-algebra A = ⊕g∈GAg is called locally finite in case each graded component Ag is finite dimensional over K. We characterize the graphs E for which the Leavitt path algebra LK(E) is

Group Gradings on Full Matrix Rings

We study G-gradings of the matrix ring Mn(k), k a field, and give a complete description of the gradings where all the elements ei, j are homogeneous, called good gradings. Among these, we determine

Methods of Graded Rings

The Category of Graded Rings.- The Category of Graded Modules.- Modules over Stronly Graded Rings.- Graded Clifford Theory.- Internal Homogenization.- External Homogenization.- Smash Products.-