TENSOR PRODUCTS OF LEAVITT PATH ALGEBRAS.

We compute the Hochschild homology of Leavitt path algebras over a field k. As an application, we show that L₂ and L₂ ⊗ L₂ have different Hochschild homologies, and so they are not Morita equivalent; in particular, they are not isomorphic. Similarly, L_∞ and L_∞ ⊗ L_∞ 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_*(L₂) = K_*(L₂ ⊗L₂) = 0 and K_*(L_∞) = X_*(L_∞ ⊗ L_∞) = K_*(k). [ABSTRACT FROM AUTHOR]