Related papers: Arithmetic-arboreal residue structures induced by …
We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for…
The resultant plays a crucial role in (computational) algebra and algebraic geometry. One of the most important and well known properties of the resultant is that it is equal to the determinant of the Sylvester matrix. In 2008, Odagiri…
In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…
The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship…
Non-trivial extensions of the three dimensional Poincar\'e algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three dimensional generalizations of fractional supersymmetry of order…
In this note we introduce a natural Finsler structure on convex surfaces, referred to as the projective Finsler structure, which is dual in a sense to the obvious inclusion of a convex surface in a normed space. It has an associated…
In this paper we will establish a structure theorem concerning the extension of analytic objects associated to germs of dimension one foliations on surfaces, through one-dimensional barriers. As an application, an extension theorem for…
Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the…
We present a constructive approximation framework for analyzing the expressive power of Fourier residual networks in approximating a broad class of one-dimensional functions. Our study covers both piecewise continuous functions -- including…
We study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and bare couplings. The residue formulas for the third derivatives…
It is well-known that an averaging operator on a commutative associative algebra gives rise to a perm algebra. This paper lifts this process to the level of bialgebras. For this purpose, we first give an infinitesimal bialgebra structure…
A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a…
The aim of this paper is to give all quasitriangular structures on a class of semisimple Hopf algebras constructed through abelian extensions of $\Bbbk\mathbb{Z}_{2}$ by $\Bbbk^G$ for an abelian group $G$. We first introduce the concept of…
Given a hypercube of Frobenius extensions between commutative algebras, we provide a diagrammatic description of some natural transformations between compositions of induction and restriction functors, in terms of colored…
We consider the intersection $\mathfrak{M}(A)$ of all maximal ideals of an evolution algebra $A$ and study the structure of the quotient $A/\M(A)$. In a previous work, maximal ideals have been related to hereditary subsets of a graph…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
We show that a weighted shift on a directed tree is related to a multiplier algebra of coefficients of analytic functions. We use this relation to study spectral properties of the operators in question.
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
We study the structures of Fourier coefficients of automorphic forms on symplectic groups based on their local and global structures related to Arthur parameters. This is a first step towards the general conjecture on the relation between…