Related papers: Hypertetrahedral arrangements

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…

We will consider some characterizations of freeness of a hyperplane arrangement, in terms of the following properties: locally freeness, factorization of characteristic polynomial and freeness of restricted multiarrangement. In the case of…

We prove automatic continuity theorems for "decomposable" or "local" linear transformations between certain natural subspaces of operator algebras. The transformations involved are not algebra homomorphisms but often are module…

We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a…

The relationship between associative composition algebras of dimensions 2 and 4 within the context of homogeneous spaces, with a particular focus on Hamiltonian quaternions, is explored. In the special case of Hamiltonian quaternions, the…

We design new tools to study variants of Total Dual Integrality. As an application, we obtain a geometric characterization of Total Dual Integrality for the case where the associated polyhedron is non-degenerate. We also give sufficient…

Let A be a generic hyperplane arrangement composed of r hyperplanes in an n-dimensional vector space, and S the polynomial ring in n variables. We consider the S-submodule D(m)(A) of the nth Weyl algebra of homogeneous differential…

In this note we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to find various relationships between non-free arrangements,…

For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…

A hyperplane arrangement is called formal provided all linear dependencies among the defining forms of the hyperplanes are generated by ones corresponding to intersections of codimension two. The significance of this notion stems from the…

Let W be a compact simply connected triangulated manifold with boundary and $K \subset W$ be a subpolyhedron. We construct an algebraic model of the rational homotopy type of the complement $W \setminus K$ out of a model of the map of pairs…

It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric…

We consider the Zariski space of all places of an algebraic function field $F|K$ of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime…

We investigate the structure of an alternative finite dimensional $\Q$-algebra $\mathfrak{A}$ subject to the condition that for a $\Z$-order $\Gamma \subset \mathfrak{A}$, and thus for every $\Z$-order of $\mathfrak{A}$, the loop of units…

A finite hypergraph $H$ consists of a finite set of vertices $V(H)$ and a collection of subsets $E(H) \subseteq 2^{V(H)}$ which we consider as partition of unity relations between projection operators. These partition of unity relations…

This is the first paper in a series on new higher categorical structures called higher Segal spaces. For every d > 0, we introduce the notion of a d-Segal space which is a simplicial space satisfying locality conditions related to…

We discuss interrelations between: Cohn localizations of full square matrices; a Leavitt localization of a row; and the Jacobson quasi-inverses of quasi-regular elements. The latter Jacobson localizations appear naturally and easily in…

In [12] was introduced, for cyclic groups, the class of partially filled arrays of the non-zero sum Heffter array that are, as the Heffter arrays, related to difference families, graph decompositions, and biembeddings. Here we generalize…

Let $G$ be a finite group and $S$ a subset of $G$. Then $S$ is product-free if $S \cap SS = \emptyset$, and complete if $G^{\ast} \subseteq S \cup SS$. A product-free set is locally maximal if it is not contained in a strictly larger…

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to…