Related papers: The Modular Stone-von Neumann Theorem

We define the localisation of a Hilbert module in analogy to the local multiplier algebra. We use properties of this localisation to enrich non-closed actions on $C^*$-algebras to closed actions on local multiplier algebras, and descend…

Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean $\ell$-algebras. In [4] we extended this duality to completely regular spaces. In this article…

We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the…

Let X be a (right) Hilbert C*-module and let B be a C*-algebra acting on X from the left via adjointable operators. In this note we establish the equivalence of two notions of nondegeneracy for such an action of B on X. Furthermore, we…

We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of properly proximal groups, we provide a number…

In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the first results which provide classes of…

Given a vector space of microscopic quantum observables, density functional theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem and the existence of the universal energy functional in the dual space are proven. In…

A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…

We prove a general criterion for a von Neumann algebra $M$ in order to be in standard form. It is formulated in terms of an everywhere defined, invertible, antilinear, a priori not necessarily bounded operator, intertwining $M$ with its…

In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra $\mathcal{A}$ into a…

Motivated by Popa's seminal work \cite{Po04}, in this paper, we provide a fairly large class of examples of group actions $\Gamma \curvearrowright X$ satisfying the extended Neshveyev-St{\o}rmer rigidity phenomenon \cite{NS03}: whenever…

A lemma stated by Ke Li in [arXiv:1208.1400] has been used in e.g. [arXiv:1510.04682,arXiv:1706.04590,arXiv:1612.01464,arXiv:1308.6503,arXiv:1602.08898] for various tasks in quantum hypothesis testing, data compression with quantum side…

We prove a double commutant theorem for separable subalgebras of a wide class of corona C*-algebras, largely resolving a problem posed by Pedersen. Double commutant theorems originated with von Neumann, whose seminal result evolved into an…

The Guillemin-Sternberg conjecture states that "quantisation commutes with reduction" in a specific technical setting. So far, this conjecture has almost exclusively been stated and proved for compact Lie groups $G$ acting on compact…

By a well known theorem of K.S. Brown an action of a discrete group on a simply-connected complex allows to construct a presentation of this group modulo the stabilizers of vertices. The main goal of the present paper is to provide a new…

The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given.

We show that a A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on appropriately defined enveloping Hilbert spaces. Applications to the theory of…

It is known to experts that certain regular inclusions of von Neumann algebras arise as crossed products with cocycle actions of the canonical quotient groupoids associated with the inclusions. Similarly, `strongly normal' inclusions of…

Given a finite type degree-wise nilpotent $L_\infty$-algebra, we construct an abelian group that acts on the set of Maurer-Cartan elements of the given $L_\infty$-algebra so that the quotient by this action becomes the moduli space of…

We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…