The matrix type of purely infinite simple Leavitt path algebras

Gene Abrams; Christopher Smith

The matrix type of purely infinite simple Leavitt path algebras

Rings and Algebras 2009-09-28 v2

Authors: Gene Abrams , Christopher Smith

Abstract

Let $R$ denote the purely infinite simple unital Leavitt path algebra $L(E)$ . We completely determine the pairs of positive integers $(c,d)$ for which there is an isomorphism of matrix rings $M_c(R)\cong M_d(R)$ , in terms of the order of $[1_R]$ in the Grothendieck group $K_0(R)$ .

Keywords

leavitt path algebra purely infinite simple matrix ring isomorphism grothendieck group k-theory

Cite

@article{arxiv.0909.3325,
  title  = {The matrix type of purely infinite simple Leavitt path algebras},
  author = {Gene Abrams and Christopher Smith},
  journal= {arXiv preprint arXiv:0909.3325},
  year   = {2009}
}

Comments

submitted version; group theory lemmas streamlined; 6 pages

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