Morita equivalence for quantum Heisenberg manifolds

Abstract

We discuss Morita equivalence within the family { D μ ν c : c ∈ Z ,   c > 0 ,   μ , ν ∈ R } \{D_{\mu \nu }^c: c\in \mathbb {Z},\ c>0,\ \mu ,\nu \in \mathbb {R}\} of quantum Heisenberg manifolds. Morita equivalence classes are described in terms of the parameters μ \mu , ν \nu and the rank of the free abelian group G μ ν = 2 μ Z + 2 ν Z + Z G_{\mu \nu }=2\mu \mathbb {Z}+2\nu \mathbb {Z}+\mathbb {Z} associated to the C ∗ C^* -algebra D μ ν c D_{\mu \nu }^{c} .