相关论文: Constructing zero divisors in the higher dimension…
Some general criteria to produce explicit free algebras inside the division ring of fractions of skew polynomial rings are presented. These criteria are applied to some special cases of division rings with natural involutions, yielding, for…
We prove a variant of the Titchmarsh convolution theorem for simply connected supersolvable Lie groups, namely we show that the convolution algebras of compactly supported continuous functions and compactly supported finite measures on such…
In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores.
In this paper we improve the level and sublevel of algebras obtained by the Cayley-Dickson process when their level and sublevel are greater than dimension of the algebras.
The division algebras R, C, H, O are used to construct and analyze the N=1,2,4,8 supersymmetric extensions of the KdV hamiltonian equation. In particular a global N=8 super-KdV system is introduced and shown to admit a Poisson bracket…
We compute generators and relations for the section ring of a rational divisor on an elliptic curve. Our technique generalizes the work of O'Dorney (in genus zero) and Voight--Zureick-Brown (for specific divisors arising from the study of…
We introduce a method for obtaining new classes of free divisors from representations $V$ of connected linear algebraic groups $G$ where $\dim(G)=\dim(V)$, with $V$ having an open orbit. We give sufficient conditions that the complement of…
Consider a nontrivial solution to a semilinear elliptic system of first order with smooth coefficients defined over an $n$-dimensional manifold. Assume the operator has the strong unique continuation property. We show that the zero set of…
We generalize Knuth's construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension $2s^2$ by doubling…
In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions were described using some spaces of functions which were defined with some…
We construct and give a complete classification of all the differential symmetry breaking operators $\mathbb{D}_{\lambda, \nu}^{N,m}: C^\infty(S^3, \mathcal{V}_\lambda^{2N+1}) \rightarrow C^\infty(S^2, \mathcal{L}_{m, \nu})$, between the…
We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…
The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and…
We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…
We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions…
As an attempt to bridge between numerical analysis and algebraic geometry, this paper formulates the multiplicity for the general nonlinear system at an isolated zero, presents an algorithm for computing the multiplicity structure, proposes…
We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…
Locating the zeros of quaternionic polynomials is a fundamental problem with significant implications across scientific and engineering disciplines, yet the noncommutative nature of quaternion multiplication makes it fundamentally more…
We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients…
We introduce the notion of a bicocycle double cross product (resp. sum) Lie group (resp. Lie algebra), and a bicocycle double cross product bialgebra, generalizing the unified products. On the level of Lie groups the construction yields a…