Related papers: On strictly nonzero integer-valued charges
Recently, Ciambelli, Leigh, and Pai (CLP) [arXiv:2111.13181] have shown that nonzero charges integrating Hamilton's equation can be defined for all diffeomorphisms acting near the boundary of a subregion in a gravitational theory. This is…
The classical theorem of Weitzenboeck states that the algebra of invariants of a single unipotent transformation $g$ in $GL_m(K)$ acting on the polynomial algebra $K[x_1,...,x_m]$ over a field $K$ of characteristic 0 is finitely generated.…
We present a new approach to singularity confinement which makes it an efficient and reliable discrete integrability detector. Our method is based on the full-deautonomisation procedure, which consists in analysing non-autonomous extensions…
We separate the $AF$-algebras (correspondingly action of the countable groups on Cantor sets) onto two classes ---- "completely smooth" for which the set of all indecomposable traces (correspondingly list of all invariant ergodic measures)…
A nowhere-zero $k$-flow on a graph $\Gamma$ is a mapping from the edges of $\Gamma$ to the set $\{\pm1, \pm2, ..., \pm(k-1)\} \subset \bbZ$ such that, in any fixed orientation of $\Gamma$, at each node the sum of the labels over the edges…
Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…
The aim of this paper is to build a theory of commutative and noncommutative {\it injective} valuations of various algebras (including algebras with zero divisors). The targets of our valuations are (well-)ordered commutative and…
A numerical semigroup $S$ is a cofinite, additively-closed subset of the nonnegative integers that contains $0$. In this paper, we initiate the study of atomic density, an asymptotic measure of the proportion of irreducible elements in a…
A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…
We propose a new "Hamiltonian inspired" covariant formula to define (without harmful ambiguities) the superpotential and the physical charges associated to a gauge symmetry. The criterion requires the variation of the Noether current not to…
A non-zero $\mathbb{F}$-valued $\mathbb{F}$-linear map on a finite dimensional $\mathbb{F}$-algebra is called an $\mathbb{F}$-valued trace if its kernel does not contain any non-zero ideals. However, given an $\mathbb{F}$-algebra such a map…
Given $A$ a set of $N$ positive integers, an old question in additive combinatorics asks that whether $A$ contains a sum-free subset of size at least $N/3+\omega(N)$ for some increasing unbounded function $\omega$. The question is generally…
We gauge the central charge of the N=2 supersymmetry algebra in rigid superspace. The Fayet Sohnius hypermultiplet with gauged central charge coincides on-shell with N=2 supersymmetric electrodynamics. The gauge couplings of the…
We derive exact relations to all orders in the $\alpha'$ expansion for the charges of a bound system of heterotic strings, solitonic 5-branes and, optionally, a Kaluza-Klein monopole. The expressions, which differ from those of the…
Hilbert's Nullstellensatz is one of the most fundamental correspondences between algebra and geometry, and has inspired a plethora of noncommutative analogs. In last two decades, there has been an increased interest in understanding…
We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…
We show that when the Wald-Zoupas prescription is implemented, the resulting charges realize the BMS symmetry algebra without any 2-cocycle nor central extension, at any cut of future null infinity. We refine the covariance prescription for…
The set of all $\ell$-zero-sumfree subsets of $\mathbb{Z}/n\mathbb{Z}$ is a simplicial complex denoted by $\Delta_{n,\ell}$ We create an algorithm via defining a set of integer partitions we call $(n,\ell)$-congruent partitions in order to…
We study the central charge of the deformed N=(1,0) supersymmetry algebra in non(anti)commutative N=2 supersymmetric U(N) gauge theory. In the cases of N=1/2 superspace and N=2 harmonic superspace with the singlet deformation, we find that…
We give a constructive proof of the general Nullstellensatz: a univariate polynomial ring over a commutative Jacobson ring is Jacobson. This theorem implies that every finitely generated algebra over a zero-dimensional ring or the ring of…