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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Tensor products of Leavitt path algebras


Authors: Pere Ara and Guillermo Cortiñas
Journal: Proc. Amer. Math. Soc. 141 (2013), 2629-2639
MSC (2010): Primary 16E40, 16S99; Secondary 19D50
Published electronically: April 25, 2013
MathSciNet review: 3056553
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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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Additional Information

Pere Ara
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
Email: para@mat.uab.cat

Guillermo Cortiñas
Affiliation: Departamento de Matemática and Instituto Santaló, Ciudad Universitaria Pab 1, 1428 Buenos Aires, Argentina
Email: gcorti@dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11561-3
Received by editor(s): August 1, 2011
Received by editor(s) in revised form: November 9, 2011
Published electronically: April 25, 2013
Additional Notes: The first author was partially supported by DGI MICIIN-FEDER MTM2008-06201-C02-01 and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya.
The second author was supported by CONICET and partially supported by grants PIP 112-200801-00900, UBACyTs X051 and 20020100100386, and MTM2007-64074.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.