Related papers: Canonical forms of oriented matroids
Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group $U_q(\mathfrak g)$ are constructed in \cite{LZ:2009} and one can use them to define some ideals of the modified quantized…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
We develop a bar involution and canonical basis for every morphism space of the oriented skein category through a diagrammatic approach. In particular, our construction gives rise to Kazhdan-Lusztig type bases on quantized walled Brauer…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
Given a positive noncommutative polynomial $f$, equivalently a sum of Hermitian squares (SOHS), there exists a positive semidefinite Gram matrix that encrypts all the structural essence of $f$. There are no available methods for extending a…
Curve singularities are classical objects of study in algebraic geometry. The key player in their combinatorial structure is the {\it value semigroup}, or its compactification, the {\it value semiring}. One natural problem is to explicitly…
An $n\times n$ symmetric matrix $A$ is copositive if the quadratic form $x^TAx$ is nonnegative on the nonnegative orthant. The cone of copositive matrices strictly contains the cone of completely positive matrices, i.e., all matrices of the…
Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique adjoint hypersurface and study them from an…
Canonical heights and Arakelov geometry on semi-abelian varieties. In this paper, we propose a construction of the canonical heights on an extension of an abelian variety by the multiplicative group, in the framework of Arakelov geometry.…
We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that…
We will start from the beginning and define a matroid and its Orlik-Solomon algebra and holonomy Lie algebra, but first we give some background from topology and cohomology. A (central) hyperplane arrangement is a finite number of subspaces…
In this article we make several contributions of independent interest. First, we introduce the notion of stressed hyperplane of a matroid, essentially a type of cyclic flat that permits to transition from a given matroid into another with…
Motivated by deformation quantization we consider $^*$-algebras over ordered rings and their deformations: we investigate formal associative deformations compatible with the $^*$-involution and discuss a cohomological description in terms…
The pure spinor superfield formalism reveals that, in any dimension and with any amount of supersymmetry, one particular supermultiplet is distinguished from all others. This "canonical supermultiplet" is equipped with an additional…
The resonance varieties, the holonomy Lie algebra, and the holonomy Chen Lie algebra associated with the Orlik-Solomon algebra of a matroid provide an algebraic lens through which to examine the rich combinatorial structure of matroids and…
I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian…
We prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from this result and a result of the third author that the positive…
In this paper we study a novel class of parabolic geometries which we call parabolic geometries of Monge type. These parabolic geometries are defined by special gradings of simple Lie algebras, namely, gradings with the property that their…
A structure M is pregeometric if the algebraic closure is a pregeometry in all M' elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of U-rank a power…
This paper is a continuation of my paper "Lattices of flats for symplectic matroids". We explore geometric constructions originating from the lattice of flats of ranked symplectic matroids. We observe that a ranked symplectic matroid always…