Related papers: Modular Completely Dirichlet forms as Squares of D…

We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of…

This paper is devoted to derivations on the algebra $S_0(M, \tau)$ of all $\tau$-compact operators affiliated with a von Neumann algebra $M$ and a faithful normal semi-finite trace $\tau.$ The main result asserts that every…

We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic).…

The Grassmann envelope is used to find the $\mathcal{N}=1$ `superquasiconformal' algebra in $D=10+1$. The adjoint representation of this algebra is found to contain $\mathfrak{su}_{2,2}\oplus \mathfrak{u}_{1}\oplus \mathfrak{su}_{5}$ as a…

The dimension of any module over an algebra of affiliated operators ${\mathcal U}$ of a finite von Neumann algebra ${\mathcal A}$ is defined using a trace on ${\mathcal A}.$ All zero-dimensional ${\mathcal U}$-modules constitute the torsion…

We show that the knowledge of the Dirichlet--to--Neumann map for a nonlinear magnetic Schr\"odinger operator on the boundary of a compact complex manifold, equipped with a K\"ahler metric and admitting sufficiently many global holomorphic…

We extend the results of Riemannian geometry over finite groups and provide a full classification of all linear connections for the minimal noncommutative differential calculus over a finite cyclic group. We solve the torsion-free and…

In this article, we prove Neveu decomposition for the action of the locally compact amenable semigroup of positive contractions on semifinite von Neumann algebras and thus, it entirely resolves the problem for the actions of arbitrary…

We prove that any weak* continuous semigroup $(T_t)_{t \geq 0}$ of factorizable Markov maps acting on a von Neumann algebra $M$ equipped with a normal faithful state can be dilated by a group of Markov $*$-automorphisms analogous to the…

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\...\ V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the…

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…

In the N=1 four-dimensional new-minimal supergravity framework, we supersymmetrise the coupling of the scalar kinetic term to the Einstein tensor. This coupling, although introduces a non-minimal derivative interaction of curvature to…

We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At the level of Teichm\"uller space, this semisimplicity…

Gauged off-shell Maxwell-Einstein supergravity in six dimensions with N=(1,0) supersymmetry has a higher derivative extension afforded by a supersymmetrized Riemann squared term. This theory admits a supersymmetric Minkowski x S^2…

We define $\Gamma_q(B,S \otimes H)$, the generalized $q$-gaussian von Neumann algebras associated to a sequence of symmetric independent copies $(\pi_j,B,A,D)$ and to a subset $1 \in S = S^* \subset A$ and, under certain assumptions, prove…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

We prove that every {\rm(}not necessarily linear nor continuous{\rm)} 2-local triple derivation on a von Neumann algebra $M$ is a triple derivation, equivalently, the set Der$_{t} (M)$, of all triple derivations on $M,$ is algebraically…

Let $K$ be an algebraic function field with constant field ${\mathbb F}_q$. Fix a place $\infty$ of $K$ of degree $\delta$ and let $A$ be the ring of elements of $K$ that are integral outside $\infty$. We give an explicit description of the…

This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…

Let G be a split connected reductive group over a finite field F_q, and N its maximal unipotent subgroup. V. Drinfeld has introduced a remarkable partial compactification of the moduli stack of N-bundles on a smooth projective curve X over…