L2,Z⊗ L2,Z does not embed in L2,Z

Authors

Nathan D. Brownlowe, University of WollongongFollow
Adam P. Sorensen, University of Oslo, University of WollongongFollow

RIS ID

105806

Publication Details

Brownlowe, N. & Sorensen, A. P W. (2016). L2,Z⊗ L2,Z does not embed in L2,Z. Journal of Algebra, 456 1-22.

Abstract

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.