For H, a Hopf coquasigroup, and A, left quasi-H-module algebra, we show that the smash product A#H is linked to algebra of H invariants AH by Morita context. We use setting prove for finite dimensional there are equivalent conditions A/AH be Galois parallel in case algebra.

Morita equivalence and T-duality (or B versus Θ) Abstract: T-duality in M(atrix) theory has been argued to be realized as Morita equivalence in Yang-Mills theory on a non-commutative torus (NCSYM). Even though the two have the same structure group, they differ in their action since Morita equivalence makes crucial use of an additional modulus on the NCSYM side, the constant Abelian magnetic bac...

One can describe an n-dimensional noncommutative torus by means of an antisymmetric n×n matrix θ. We construct an action of the group SO(n, n|Z) on the space of n× n antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched. By definition [R5], an n-dimensional noncommutative torus...

With every (strict or normal) unital endomorphism of the algebra of all adjointable operators on a Hilbert module there is associated a correspondence (that is, a Hilbert bimodule) such that the endomorphism can be recovered as amplification of the identity representation with that correspondence. In these notes we show the converse of this statement in the case of strongly full W–correspondenc...

Article history: Received 7 March 2013 Available online xxxx Communicated by Changchang Xi

We prove that two semigroups with local units are Morita equivalent if and only if they have a joint enlargement. This approach to Morita theory provides a natural framework for understanding McAlister’s theory of the local structure of regular semigroups. In particular, we prove that a semigroup with local units is Morita equivalent to an inverse semigroup precisely when it is a regular locall...

We give a solution, via operator spaces, of an old problem in the Morita equivalence of C*-algebras. Namely, we show that C*-algebras are strongly Morita equivalent in the sense of Rieffel if and only if their categories of left operator modules are isomorphic via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (=...