%0 Journal Article
%T Tensor products of Leavitt path algebras
%A Pere Ara
%A Guillermo Corti£¿as
%J Mathematics
%D 2011
%I arXiv
%R 10.1090/S0002-9939-2013-11561-3
%X We compute the Hochschild homology of Leavitt path algebras over a field $k$. As an application, we show that $L_2$ and $L_2\otimes L_2$ have different Hochschild homologies, and so they are not Morita equivalent; in particular they are not isomorphic. Similarly, $L_\infty$ and $L_\infty\otimes L_\infty$ 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 $K_*(L_2)=K_*(L_2\otimes L_2)=0$ and $K_*(L_\infty)=K_*(L_\infty\otimes L_\infty)=K_*(k)$.
%U http://arxiv.org/abs/1108.0352v3