Leavitt $R$-algebras over countable graphs embed into $L_{2,R}$

Abstract

For a commutative ring $R$ with unit we show that the Leavitt path algebra $L_R(E)$ of a graph $E$ embeds into $L_{2,R}$ precisely when $E$ is countable. Before proving this result we prove a generalised Cuntz-Krieger Uniqueness Theorem for Leavitt path algebras over $R$.

17 pages. At the request of a referee the previous version of this paper has been split into two papers. This version is the first of these papers. The second will also be uploaded to the arXiv

References in corpus (1)

• $L_{2,\mathbb{Z}}\otimes L_{2,\mathbb{Z}}$ does not embed in $L_{2,\mathbb{Z}}$

Cited by in corpus (5)

• Amenability and uniform Roe algebras
• Topological Full Groups of Ample Groupoids with Applications to Graph Algebras
• Amenability of coarse spaces and K-algebras
• $L_{2,\mathbb{Z}}\otimes L_{2,\mathbb{Z}}$ does not embed in $L_{2,\mathbb{Z}}$
• Homotopy classification of Leavitt path algebras