L2,Z⊗ L2,Z does not embed in L2,Z
For a commutative ring R with unit we investigate the embedding of tensor product algebras into the Leavitt algebra L2,R. We show that the tensor product L2,Z⊗L2,Z does not embed in L2,Z (as a unital *-algebra). We also prove a partial non-embedding result for the more general L2,R⊗L2,R. Our techniques rely on realising Thompson's group V as a subgroup of the unitary group of L2,R.