Related papers: A short survey on observability
The polynomial affine model of gravity was proposed as an alternative to metric and metric-affine gravitational models. What at the beginning was thought as a source of unpredictability, the presence of many terms in the action, turned out…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
In this fourth of our series of papers on observables we show that one can associate to each von Neumann algebra R a pair of isomorphic presheaves, the upper presheaf O^{+}_{R} and the lower presheaf O^{-}_{R}, on the category of abelian…
We propose an algebraic study of the simple graph isomorphism problem. We define a Hopf algebra from an explicit realization of its elements as formal power series. We show that these series can be evaluated on graphs and count occurrences…
A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which generalises a result obtained for finite groups by W. Gasch\"utz…
Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^*$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$,…
Let G be a group and f be an endomorphism of G. A subgroup H of G is called f-inert if the meet of Hf and H has finite index in the image Hf. The subgroups that are f-inert for all inner automorphisms of G are widely known and studied in…
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field…
The notion of multiplicity of a module first arose as consequence of Hilbert's work on commutative algebra, relating the dimension of rings with the degree of certain polynomials. For noncommutative rings, the notion of multiplicity first…
In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…
Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…
We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal…
The supersymmetric version of a topological quantum field theory describing flat connections, the super BF-theory, is studied in the superspace formalism. A set of observables related to topological invariants is derived from the curvature…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
We study slow-roll inflation as a common feature in Metric-affine Theories of Gravity. In particular, we take into account extended metric, teleparallel and symmetric-teleparallel theories of gravity, based on different geometric…