English

The Leavitt path algebra of a graph

Rings and Algebras 2007-05-23 v1

Abstract

For any row-finite graph EE and any field KK we construct the {\its Leavitt path algebra} L(E)L(E) having coefficients in KK. When KK is the field of complex numbers, then L(E)L(E) is the algebraic analog of the Cuntz Krieger algebra C(E)C^*(E) described in [8]. The matrix rings Mn(K)M_n(K) and the Leavitt algebras L(1,n) appear as algebras of the form L(E)L(E) for various graphs EE. In our main result, we give necessary and sufficient conditions on EE which imply that L(E)L(E) is simple.

Keywords

Cite

@article{arxiv.math/0509494,
  title  = {The Leavitt path algebra of a graph},
  author = {G. Abrams and G. Aranda Pino},
  journal= {arXiv preprint arXiv:math/0509494},
  year   = {2007}
}
R2 v1 2026-07-22T17:24:48.173Z