TY - JOUR
T1 - Tensor products of Leavitt path algebras
AU - Cortiñas, Guillermo
AU - Ara, Pere
PY - 2013/8/1
Y1 - 2013/8/1
N2 - 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.
AB - 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.
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=4247710
UR - https://www.scopus.com/pages/publications/84878207665
U2 - 10.1090/S0002-9939-2013-11561-3
DO - 10.1090/S0002-9939-2013-11561-3
M3 - Article
SN - 0002-9939
VL - 141
SP - 2629
EP - 2639
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 8
ER -