We characterize the pairs of operator spaces which occur as pairs of Morita equivalence bimodules between non-selfadjoint operator algebras in terms of the mutual relation between the spaces. We obtain a characterization of the operator spaces which are completely isometrically isomorphic to imprimitivity bimodules between some strongly Morita equivalent (in the sense of Rieffel) C*-algebras. A...

We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (= interior tensor product) with a strong Morita equivalence bimodule. Date: Septembe...

We give a necessary condition for Morita equivalence of simple Generalized Weyl algebras of classical type. We propose a reformulation of Hodges’ result, which describes Morita equivalences in case the polynomial defining the Generalized Weyl algebra has degree 2, in terms of isomorphisms of quantum tori, inspired by similar considerations in noncommutative differential geometry. We study how f...

We give a condition on a full coaction (A,G, δ) of a (possibly) nonamenable group G and a closed normal subgroup N of G which ensures that Mansfield imprimitivity works; i.e. that A×δ| G/N is Morita equivalent to A×δ G×δ̂,r N . This condition obtains if N is amenable or δ is normal. It is preserved under Morita equivalence, inflation of coactions, the stabilization trick of Echterhoff and Raebur...

We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary homotopy for functors. The 1-homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the notion of orbifold 1-homotopy type induced by a 1-homotopy between presentations of the orbif...

In this note we show that two nite dimensional algebras have the same representation type if they are stably equivalent of Morita type. Stable equivalences of Morita type were introduced for blocks of group algebras by Brou e 2], see also 7]. The concept is motivated by a result of Rickard. In 9], he proved that any derived equivalence between nite dimensional self-injective algebras and ? indu...