Related papers: On invariant random positive definite functions
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variational problems, we consider group actions…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The…
We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.
Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the alternating invariant functions. Examples of such functions…
On a finite structure, the polymorphism invariant relations are exactly the primitively positively definable relations. On infinite structures, these two sets of relations are different in general. Infinitary primitively positively…
Given an action $\alpha$ of a discrete group $G$ on a unital C*-algebra $A$, we introduce a natural concept of $\alpha$-negative definiteness for functions from $G$ to $A$, and examine some of the first consequences of such a notion. In…
Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
For a broad class of Frechet-Lie supergroups we prove that there exists a correspondence between positive definite smooth superfunctions and matrix coefficients of unitary representations. We also give a characterization of linear…
In a previous study, the first author defines an inverse ambiguous function on a group $G$ to be a bijective function $f : G \to G$ satisfying the functional equation $f^{-1}(x) = f(x^{-1})$ for all $x \in G$. In this paper, we investigate…
It is shown that a real-valued formal meromorphic function on a formal generic submanifold of finite Kohn-Bloom-Graham type is necessarily constant.
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
In this note we study a natural analytic property of inclusions of groups akin to co-amenability: the property of existence of a non-compactly supported invariant state for the conjugation action of a group $G$ on the von Neumann algebra…
Let $\mathbb{N}$ be a set of the natural numbers. Symmetric inverse semigroup $R_\infty$ is the semigroup of all infinite 0-1 matrices $\left[ g_{ij}\right]_{i,j\in \mathbb{N}}$ with at most one 1 in each row and each column such that…
We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…
In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…
We define entropy invariants for abstract algebraic structures using an asymptotic Boltzmann formula.
We prove a number of results linking properties of actions by compact groups (both quantum and classical) on Banach spaces, such as uniform continuity, spectrum finiteness and extensibility of the actions across several constructions.…