L 2 , Z ⊗ L 2 , Z does not embed in L 2 , Z

2016/03/03 by Nathan Brownlowe, Adam P. W. Sørensen, Adam P W Sørensen
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Artificial intelligence #Computer science #Embedding #Geometry #Mathematics #Product (mathematics) #Pure mathematics #Tensor product #math.OA #math.RA

paper · pdf · doi:10.1016/j.jalgebra.2016.01.040

published as Journal of Algebra, Volume 456, 15 June 2016, Pages 1-22 · 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

openalex publication_date 2016/03/03 · arxiv created 2016/03/11 · arxiv updated 2016/03/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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,ℤ⊗ L_2,ℤ does not embed in L_2,ℤ (as a unital *-algebra). We also prove a partial non-embedding result for the more general L_2,R ⊗ L_2,R. Our techniques rely on realising Thompson's group V as a subgroup of the unitary group of L_2,R.

Citations

• Leavitt R-algebras over countable graphs embed into L_2,R
• K-Theory for Operator Algebras
• The Cuntz splice does not preserve *-isomorphism of Leavitt path algebras over ℤ