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arXiv · 1108.0352

Tensor products of Leavitt path algebras

Pere Ara·Guillermo Cortiñas
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Abstract

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 $K_*(L_\infty)=K_*(L_\infty\otimes L_\infty)=K_*(k)$.

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Pere Ara, Guillermo Cortiñas. 2011-08-01. Tensor products of Leavitt path algebras. https://doi.org/10.1090/s0002-9939-2013-11561-3

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