Related papers: On strictly nonzero integer-valued charges
To study the set of torsion classes of a finite dimensional basic algebra, we use a decomposition, called sign-decomposition, parametrized by elements of $\{\pm1\}^n$ where $n$ is the number of simple modules. If $A$ is an algebra with…
In algebraic number theory, the finiteness of the Picard group of an order in a number field is generally proved via a lattice argument: the order forms a lattice and every ideal class contains an integral ideal with a small enough non-zero…
We define a class of associative algebras generalizing 'clannish algebras', as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well known 'string…
Let $G= SL_{n+1}$ be defined over an algebraically closed field of characteristic $p > 2$. For each $n \geq 1$ there exists a singular block in the category of $G_1$-modules which contains precisely $n+1$ irreducible modules. We are…
We derive a set of recursion formulae to construct singular vectors for the $N=2$ (untwisted) algebra, by using the approach of Bauer, di Francesco, Itzykson and Zuber. Applying these formulae, we obtain explicit expressions for the charged…
We propose a simple approximation scheme to compute the effective charge of highly charged colloids (spherical or cylindrical with infinite length). Within non-linear Poisson-Boltzmann theory, we start from an expression of the effective…
In the zero-error Slepian-Wolf source coding problem, the optimal rate is given by the complementary graph entropy $\overline{H}$ of the characteristic graph. It has no single-letter formula, except for perfect graphs, for the pentagon…
The Skolem Problem asks to determine whether a given integer linear recurrence sequence has a zero term. This problem arises across a wide range of topics in computer science, including loop termination, formal languages, automata theory,…
We prove that any Boolean algebra with the subsequential completeness property contains an independent family of size continuum. This improves a result of Argyros from the 80ties which asserted the existence of an uncountable independent…
We prove that assuming suitable cardinal arithmetic, if B is a Boolean algebra every homomorphic image of which is isomorphic to a factor, then B has locally small density. We also prove that for an (infinite) Boolean algebra B, the number…
On an arbitrary meet-semilattice S with 0 we define an orthogonality relation and investigate the lattice Cl(S) of all subsets of S closed under this orthogonality. We show that if S is atomic then Cl(S) is a complete atomic Boolean…
This article explores the concept of absoluteness in the context of mathematical analysis, focusing specifically on the Riemann integral on $\mathbb{R}^{n}$. In mathematical logic, "absoluteness" refers to the invariance of the truth value…
The non-integrable mass is studied explicitly in this paper. We study Einstein-scalar gravities with weakened boundary conditions, and calculate the mass with the Hamiltonian formula and Wald's formula respectively. We find the masses…
Using a formalism of minitwistors, we derive infinitely many conserved charges for the $sl(\infty )$-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite…
The conserved charges associated to gauge symmetries are defined at a boundary component of space-time because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is…
In this paper we make a proposal for the solution to a long-standing problem - the asymptotic expansions of the modular $S$-transform of a generalised Gibbs ensemble (GGE) in a theory with $\mathcal{W}_3$ symmetry where the GGE includes the…
A subset $A$ of a Boolean algebra $B$ is said to be $(n,m)$-reaped if there is a partition of unity $P \subset B$ of size $n$ such that the cardinality of $\{b \in P: b \wedge a \neq \emptyset\}$ is greater than or equal to $m$ for all…
A set $M$ of nonzero integers is said to split a finite abelian group $G$ if there exists a subset $S\subseteq G$ such that $M\cdot S = G\setminus\{0\}$. Such a splitting is called purely singular if every prime divisor of $|G|$ divides…
Within the framework of Euclidean path integral and mass perturbation theory we compute the Wilson loop of widely separated external charges for the massive Schwinger model. From this result we show for arbitrary order mass perturbation…
An algebra is said to be quasi-directly finite when any left-invertible element in its unitization is automatically right-invertible. It is an old observation of Kaplansky that the von Neumann algebra of a discrete group has this property;…