Tensor products of Leavitt path algebras

Pere Ara, Guillermo Cortiñas

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

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*(L*2) = K*(L2 ⊗ L2) = 0 and K*(L∞) = K*(L∞ ⊗ L∞) = K*(k). © 2012 American Mathematical Society.
Original languageEnglish
Pages (from-to)2629-2639
JournalProceedings of the American Mathematical Society
Volume141
Issue number8
DOIs
Publication statusPublished - 1 Aug 2013

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