Related papers: Splitting fields of differential symbol algebras

A digraph is called an $n$-Cayley digraph if its automorphism group has an $n$-orbit semiregular subgroup. We determine the splitting fields of $n$-Cayley digraphs over abelian groups and compute a bound on their algebraic degrees, before…

Finite nonassociative division algebras (i.e., finite semifields) with 243 elements are completely classified.

Given a field $F$, an \'etale extension $L/F$ and an Azumaya algebra $A/L$, one knows that there are extensions $E/F$ such that $A \otimes_F E$ is a split algebra over $L \otimes_F E$. In this paper we bound the degree of a minimal…

We described all \delta-derivations of semisimple f.-d. structurable algebras over algebraically closed field with characteritic is not equal 2,3,5.

We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…

We study the structure of arbitrary split Leibniz superalgebras. We show that any of such superalgebras ${\frak L}$ is of the form ${\frak L} = {\mathcal U} + \sum_jI_j$ with ${\mathcal U}$ a subspace of an abelian (graded) subalgebra $H$…

This paper gives two results on the simple modules for the Brauer algebra over the complex field. First we describe the module structure of the restriction of all simple modules. Second we give a new geometrical interpretation of Ram and…

Let $\mathcal{X}$ be a projective algebraic curve and denote by $\mathcal{X}^{'}$ its strict dual curve. The map $\gamma:\mathcal{X} \longrightarrow \mathcal{X}^{'}$ is called (strict) Gauss map of $\mathcal{X}$. In this manuscript, we…

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is…

We introduce and study the concept which we call the splitting of a graph and compare algebraic properties of the edge ideals of graphs and those of their splitting graphs.

Given a field $F$ of characteristic $3$ and division symbol $p$-algebras $[\alpha,\beta)_{3,F}$ and $[\alpha,\gamma)_{3,F}$ of degree $3$ over $F$, we prove that if $\alpha \text{dlog}(\beta)\wedge \text{dlog}(\gamma)$ is trivial in the…

Semialgebraic splines are functions that are piecewise polynomial with respect to a cell decomposition into sets defined by polynomial inequalities. We study bivariate semialgebraic splines, formulating spaces of semialgebraic splines in…

We show in this article that in many cases the subfields of a nondegenerate tame semiramified division algebra of prime power degree over a Henselian valued field are inertial field extensions of the center.

An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many…

We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…

Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph…

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra…

A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.