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Morita Base Change in Hopf-Cyclic (Co)Homology

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Abstract

In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invariance for cyclic homology of associative algebras appears as a special example of this theory. In our main application we consider the Morita equivalence between the algebra of complex-valued smooth functions on the classical 2-torus and the coordinate algebra of the noncommutative 2-torus with rational parameter. We then construct a Morita base change left Hopf algebroid over this noncommutative 2-torus and show that its cyclic (co)homology can be computed by means of the homology of the Lie algebroid of vector fields on the classical 2-torus.

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Authors and Affiliations

  1. Departamento de Álgebra, Facultad de Educación y Humanidades de Ceuta, Universidad de Granada, El Greco No. 10, 51002, Ceuta, Spain

    Laiachi El Kaoutit

  2. Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Niels Kowalzig

Authors
  1. Laiachi El Kaoutit
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  2. Niels Kowalzig
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Correspondence to Niels Kowalzig.

Additional information

Research of L. El Kaoutit was supported by the grant MTM2010-20940-C02-01 from the Ministerio de Ciencia e Innovación and from FEDER. N. Kowalzig acknowledges funding by the Excellence Network of the University of Granada (GENIL).

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El Kaoutit, L., Kowalzig, N. Morita Base Change in Hopf-Cyclic (Co)Homology. Lett Math Phys 103, 665–699 (2013). https://doi.org/10.1007/s11005-012-0600-7

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  • DOI: https://doi.org/10.1007/s11005-012-0600-7

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