The Cuntz splice does not preserve $\ast$-isomorphism of Leavitt path algebras over $\mathbb{Z}$

Rune Johansen, Adam P. W. Sørensen

We show that the Leavitt path algebras $L_{2,\mathbb{Z}}$ and $L_{2-,\mathbb{Z}}$ are not isomorphic as $\ast$-algebras. There are two key ingredients in the proof. One is a partial a…