Related papers: Geometric algebra of projective lines
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
In this paper, we consider the groupoidification of the fermion algebra. We construct a groupoid as the categorical analogues of the fermionic Fock space, and the creation and annihilation operators correspond to spans of groupoids. The…
A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We…
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
In this paper we further the study of arrow algebras, simple algebraic structures inducing toposes through the tripos-to-topos construction, by defining appropriate notions of morphisms between them which correspond to morphisms of the…
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.
We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.
Linear Geometry describes geometric properties that depend on the fundamental notion of a line. In this paper we survey basic notions and results of Linear Geomery that depend on the flat hulls: flats, exchange, rank, regularity,…
Given a category, one may construct slices of it. That is, one builds a new category whose objects are the morphisms from the category with a fixed codomain and morphisms certain commutative triangles. If the category is a groupoid, so that…
We discuss the relationship between geometry, the renormalization group (RG) and gravity. We begin by reviewing our recent work on crossover problems in field theory. By crossover we mean the interpolation between different representations…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad…
We formulate a relative, representation theoretic, notion of the algebraic cone construction. This motivates a generalization of the cone corresponding to a preprojective algebra.
We conjecture the existence of a simple geometric structure underlying questions of reducibility of parabolically induced representations of reductive p-adic groups.
On a projective complex manifold, the Abelian group of Divisors maps surjectively onto that of holomorphic line bundles (the Picard group). On a $G_2$-manifold we use coassociative submanifolds to define an analogue of the first, and a…
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…