Abstract We consider two inclusions of $C^{*}$ -algebras whose small have approximate units the large and their spaces all bounded bimodule linear maps. suppose that are strongly Morita equivalent. In this paper, we shall show there exists an isometric isomorphism from one maps to other space study basic properties about isomorphism. And, using isomorphism, define Picard group for a map discuss...

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

In this paper, we study the Morita context for arbitrary semigroups. We prove that, for two semigroups S and T, if there exists a Morita context (S, T, P,Q, τ, μ) (not necessary unital) such that the maps τ and μ are surjective, the categories US-FAct and UT -FAct are equivalent. Using this result, we generalize Theorem 2 in [2] to arbitrary semigroups. Finally, we give a characterization of Mo...

Mackey’s imprimitivity theorem characterises the unitary representations of a locally compact group G which have been induced from representations of a closed subgroupK; Rieffel’s influential reformulation says that the group C-algebra C(K) is Morita equivalent to the crossed product C0(G/K) × G [14]. There have since been many important generalisations of this theorem, especially by Rieffel [1...

2 Poisson geometry and some generalizations 3 2.1 Poisson manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Dirac structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Twisted structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Symplectic leaves and local structure of Poisson manifolds ...

In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field k and modules over an algebra are finitely generated left unitary modules. Let A and B be two algebras (where k is a splitting field for A and B) with no semisimple summands. If two bimodules AMB and BNA induce a stable equivalence of Morita type between A and B, and if N⊗A− maps any simple A-module...