Related papers: Swiss Cheeses and Their Applications
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
We lift the Lefschetz number from an algebraic invariant of maps between spaces to an invariant of morphisms of data over the spaces.
This paper makes contributions to ``pure'' sheaf model theory, the part of model theory in which the models are sheaves over a complete Heyting algebra. We start by outlining the theory in a way we hope is readable for the non-specialist.…
We study the differential geometric consequences of our previous result on the existence of fat triangulations, in conjunction with a result of Cheeger, M\"{u}ller and Schrader, regarding the convergence of Lipschitz-Killing curvatures of…
This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…
Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We…
We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We describe a positive characteristic analogue of the Kazhdan-Lusztig basis of the Hecke algebra of a crystallographic Coxeter system and investigate some of its properties. Using Soergel calculus we describe an algorithm to calculate this…
Schneider-Stuhler and Vigneras have used cosheaves on the affine Bruhat-Tits building to construct natural finite type projective resolutions for admissible representations of reductive p-adic groups in characteristic not equal to p. We use…
Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer groups that commutes with restriction. We additionally…
Recent work by a number of people has shown that complex reflection groups give rise to many representation-theoretic structures (e.g., generic degrees and families of characters), as though they were Weyl groups of algebraic groups.…
In approximation theory classical discrete operators, like generalized sampling, Sz\'{a}sz-Mirak'jan, Baskakov and Bernstein operators, have been extensively studied for scalar functions. In this paper, we look at the approximation of…
We introduce symplectic left Leibniz algebras and symplectic right Leibniz algebras as generalizations of symplectic Lie algebras. These algebras possess a left symmetric product and are Lie-admissible. We describe completely symmetric…
A modified definition of the category of forests by Costello and expounded upon by Getzler is given. This language is used to prove some cofibration properties of the W construction for colored operads, following the work of…
We give a description of the value of a finitary localizing invariant, such as algebraic $K$-theory, on the category of sheaves on a locally coherent space $X$. This in particular includes all spaces that arise as spectra of commutative…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation…
This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras,…
The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…