Tensor products of Leavitt path algebras.

PERE ARA; GUILLERMO CORTIÑAS

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Lugar: Providence; Año: 2013 vol. 141 p. 2629 - 2639

0002-9939

We compute the Hochschild homology of Leavitt path algebras over a field $k$. As an application, we show that $L_2$ and $L_2otimes L_2$ have different Hochschild homologies, and so they are not Morita equivalent; in particular they are not isomorphic. Similarly, $L_infty$ and $L_inftyotimes L_infty$ are distinguished by their Hochschild homologies and so they are not Morita equivalent either. By contrast, we show that $K$-theory cannot distinguish these algebras; we have $K_*(L_2)=K_*(L_2otimes L_2)=0$ and $K_*(L_infty)=K_*(L_inftyotimes L_infty)=K_*(k)$.