Morita base change in Hopf-cyclic (co)homology

Details Morita base change in Hopf-cyclic (co)homology Morita base change in Hopf-cyclic (co)homology

2011-11-16

arxiv.org/abs/1111.3890v1

Mathematics

Quantum Algebra

27 pages

Scientific paper

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. We then construct a Morita base change (4 X 4)-matrix left Hopf algebroid over the 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 over the classical 2-torus.

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