Related papers: Vector Groupoids
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.
We briefly review our results on the Lie theory underlying vector bundles over Lie groupoids and Lie algebroids, pointing out the role of Poisson geometry in extending these results to double Lie algebroids and LA-groupoids.
In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each orbigroupoid represents an orbispace, but just as with…
Let $V$ be an algebraic variety defined over $\mathbb R$, and $V_{top}$ the space of its complex points. We compare the algebraic Witt group $W(V)$ of symmetric bilinear forms on vector bundles over $V$, with the topological Witt group…
The aim of this paper is to investigate the point spectra of vector fields. We will define the point spectrum of a vector field and study some of its basic properties. In particular, we will prove that point spectra are well-behaved under…
Q-groupoids and Q-algebroids are, respectively, supergroupoids and superalgebroids that are equipped with compatible homological vector fields. These new objects are closely related to the double structures of Mackenzie; in particular, we…
This paper constructs a representation of a Hecke algebra on a vector space spanned by the involutions in a Coxeter group.
This is the first in a series of articles devoted to providing a foundation for a theory of flocks of arbitrary cones in PG(3,q). The desire to have such a theory stems from a need to better understand the very significant and applicable…
Motivated by Quantum Mechanics considerations, we expose some cross product constructions on a groupoid structure. Furthermore, critical remarks are made on some basic formal aspects of the Hopf algebra structure.
The interplay between groups and graphs have been the most famous and productive area of algebraic graph theory. In this paper, we introduce and study the graphs whose vertex set is group G such that two distinct vertices a and b having…
In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.
This paper deals with a class of Sobolev spaces of vector-valued functions on a compact group. Some Sobolev embedding theorems are proved.
We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.
In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…
The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…
Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and…
A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…