相关论文: Random Operators and Crossed Products
We study spectral properties of random operators in the general setting of groupoids and von Neumann algebras. In particular, we establish an explicit formula for the canonical trace of the von Neumann algebra of random operators and define…
We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed.…
We carry out a careful study of basic topological and ergodic features of Delone dynamical systems. We then investigate the associated topological groupoids and in particular their representations on certain direct integrals with non…
Recent work has highlighted the importance of crossed products in correctly elucidating the operator algebraic approach to quantum field theories. In the gravitational context, the crossed product simultaneously promotes von Neumann…
In this paper we introduce the crossed product construction for a discrete group action on an operator system. In analogy to the work of E. Katsoulis and C. Ramsey, we describe three canonical crossed products arising from such a dynamical…
Expanding on previous work of the author, we initiate the model theoretic study of W$^*$-dynamical systems. We axiomatize continuous weight-preserving group actions of $G$ on von Neumann algebras for $G$ a given locally compact Hausdorff…
We give a survey of recent classification results for crossed product von Neumann algebras arising from measure preserving group actions on probability spaces. This includes II_1 factors with uncountable fundamental groups and the…
We propose a generalisation of Exel's crossed product by a single endomorphism and a transfer operator to the case of actions of abelian semigroups of endomorphisms and associated transfer operators. The motivating example for our…
We study the relationship between the dynamics of the action $\alpha$ of a discrete group $G$ on a von Neumann algebra $M$, and structural properties of the associated crossed product inclusion $L(G) \subseteq M \rtimes_\alpha G$, and its…
We introduce a traceable operator-algebraic framework for incompressible transport on M= T3 (and, more generally, compact Riemannian manifolds endowed with a smooth invariant probability measure). Given an autonomous divergence-free…
von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a…
The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…
We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when…
We consider the tracial crossed product algebra $M=A\rtimes\Lambda$ arising from a trace preserving action $\sigma:\Lambda \curvearrowright A$ of a discrete group $\Lambda$ on a tracial von Neumann algebra $A$. For a unitary subgroup…
We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for…
For $\MvN$ a separable, purely infinite von Neumann algebra with almost periodic weight $\phi$, a decomposition of $\MvN$ as a crossed product of a semifinite von Neumann algebra by a trace--scaling action of a countable abelian group is…
We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…
Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…
An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III$_1$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states.…
We consider crossed product von Neumann algebras arising from free Bogoljubov actions of the integers. We describe several presentations of them as amalgamated free products and cocycle crossed products and give a criterion for…