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 Hochsch...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/14840 |
| Acceso en línea: | http://hdl.handle.net/11336/14840 |
| Access Level: | acceso abierto |
| Palabra clave: | Leavitt Path Algebras Cuntz-Krieger Algebras Hochschild Homology K-Theory https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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∞) = K∗(L∞ ⊗ L∞) = K∗(k). |
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