A Bicategorical Approach to Morita Equivalence for Rings and von Neumann Algebras

Morita Theory for Derived Categories: a Bicategorical Perspective

We present a bicategorical perspective on derived Morita theory for rings, DG algebras, and spectra. This perspective draws a connection between Morita theory and the bicategorical Yoneda Lemma, yielding a conceptual unification of Morita theory in derived and bicategorical contexts. This is motivated by study of Rickard’s theorem for derived equivalences of rings and of Morita theory for ring ...

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Operator Algebras and Poisson Manifolds Associated to Groupoids

It is well known that a measured groupoid G defines a von Neumann algebra W ∗(G), and that a Lie groupoid G canonically defines both a C∗-algebra C∗(G) and a Poisson manifold A∗(G). We construct suitable categories of measured groupoids, Lie groupoids, von Neumann algebras, C∗-algebras, and Poisson manifolds, with the feature that in each case Morita equivalence comes down to isomorphism of obj...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.