Related papers: Von Neumann Categories
Rings form a bicategory [Rings], with classes of bimodules as horizontal arrows, and bimodule maps as vertical arrows. The notion of Morita equivalence for rings can be translated in terms of bicategories in the following way. Two rings are…
The theory of $N$-complexes is a generalization of both ordinary chain complexes and graded objects. Hence it yields deeper insight in the structure of these and offers a broader range of applications. This work generalizes the tensor…
In this paper we describe the amalgamated free product of finite and semifinite hyperfinite von Neumann algebras over atomic type I subalgebras. To do this we extend the notions of free dimension and standard embeddings used in the related…
If \{A(V)\} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V_1 and V_2 are spacelike separated spacetime regions, then the system (A(V_1),A(V_2),\phi) is said to satisfy…
In this paper we introduce the notion of (pointed) prenormal category, modelled after regular categories, but with the key notions of coequaliser and kernel pair replaced by those of cokernel and kernel. This framework provides a natural…
We study (von Neumann) regular $^*$-subalgebras of $B(H)$, which we call R$^*$-algebras. The class of R$^*$-algebras coincides with that of "E$^*$-algebras that are pre-C$^*$-algebras" in the sense of Z. Sz\H{u}cs and B. Tak\'acs. We give…
In Fritz & Rischel, Infinite products and zero-one laws in categorical probability, the problem was posed of finding an interesting Markov category which is causal and has all (small) Kolmogorov products (there Problem 6.7). Here we give an…
In this paper, we define a family of categories for each Liouville manifold, which is an enhanced version of the category first introduced by Tamarkin. Using our categories, for any (possibly non-exact immersed) Lagrangian brane, we develop…
We classify C$^*$ near-group categories by using Vaughan Jones theory of subfactors and the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between two essentially different cases, integral and irrational cases.…
In this paper, we propose a new construction of vertex algebras using the Deligne category. This approach provides a rigorous framework for defining the so-called large $N$ vertex algebra, which has appeared in recent physics literatures.…
This paper addresses a conjecture of Kadison and Kastler that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N and, moreover, the implementing unitary can be chosen…
In this work we give a generalization of matched pairs of (finite) groups to describe a general class of depth two inclusions of factor von Neumann algebras and the C*-quantum groupoids associated with, using double groupoids.
We introduce a general categorical framework for finiteness conditions that unifies classical notions such as Noetherianness, Artinianness, and various forms of topological compactness. This is achieved through the concept of…
In the mid thirties Murray and von Neumann found a natural way to associate a von Neumann algebra $L(\Gamma)$ to any countable discrete group $\Gamma$. Classifying $L(\Gamma)$ in term of $\Gamma$ is a notoriously complex problem as in…
Given a unitary fusion category, one can define the Hilbert space of a so-called ``anyonic spin-chain'' and nearest neighbor Hamiltonians providing a real-time evolution. There is considerable evidence that suitable scaling limits of such…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
An algebraic quantum field theory (AQFT) may be expressed as a functor from a category of spacetimes to a category of algebras of observables. However, a generic category $\mathsf{C}$ whose objects admit interpretation as spacetimes is not…
Noncommutative near-group fusion categories were completely classified in the previous work of the first named author by using an operator algebraic method (and hence under the assumption of unitarity), and they were shown to be group…
The single-trace, infinite-N algebra of an arbitrary region may or may not be a von Neumann algebra depending on the GNS sector. In this paper we identify the holographic dual of this mechanism as a consequence of the focusing of null…
By means of the notions of cross product algebras of the theory of quantum groups, in the context of classical Hopf algebra structures, we deduce some known structures of Weyl algebras type (as the Drinfeld quantum double, the restricted…