On a conformal net 𝒜, one can consider collections of unital completely positive maps on
each local algebra 𝒜 (I), subject to natural compatibility, vacuum preserving and conformal …

We prove that a haploid associative algebra in a C∗-tensor category C is equivalent to a Q-
system (a special C∗-Frobenius algebra) in C if and only if it is rigid. This allows us to prove …

For a group G and ω ∈ Z^ 3 (G, U (1)) ω∈ Z 3 (G, U (1)), an ω ω-anomalous action on a C*-
algebra B is a U (1) U (1)-linear monoidal functor between 2-groups, where the latter …

In the first part of this paper, we give a newlook at inclusions of von Neumann algebras with
finite-dimensional centers and finite Jones' index. The minimal conditional expectation is …

We show that the generator of a GNS-symmetric quantum Markov semigroup can be written
as the square of a derivation. This generalizes a result of Cipriani and Sauvageot for tracially …

Discrete subfactors include a particular class of infinite index subfactors and all finite index
ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity …

We prove that every rigid C⁎-bicategory with finite-dimensional centers (finitely
decomposable horizontal units) can be realized as Connes' bimodules over finite direct …

Let 𝒩⊂ ℳ be a unital inclusion of arbitrary von Neumann algebras. We give a 2-C∗-
categorical/planar algebraic description of normal faithful conditional expectations E: ℳ→ …

The notion of index for inclusions of von Neumann algebras goes back to a seminal work of
Jones on subfactors of type ${I\! I} _1 $. In the absence of a trace, one can still define the …