$L_{2,\mathbb{Z}} \otimes L_{2,\mathbb{Z}}$ does not embed in $L_{2,\mathbb{Z}}$
Abstract
For a commutative ring $R$ with unit we investigate the embedding of tensor product algebras into the Leavitt algebra $L_{2,R}$. We show that the tensor product $L_{2,\mathbb{Z}}\otimes L_{2,\mathbb{Z}}$ does not embed in $L_{2,\mathbb{Z}}$ (as a unital $*$algebra). We also prove a partial nonembedding result for the more general $L_{2,R} \otimes L_{2,R}$. Our techniques rely on realising Thompson's group $V$ as a subgroup of the unitary group of $L_{2,R}$.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.03618
 Bibcode:
 2016arXiv160303618B
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Operator Algebras
 EPrint:
 16 pages. At the request of a referee the paper arXiv:1503.08705v2 was split into two papers. This is the second of those papers