Related papers: Partial inner product spaces: Some categorical asp…

This is a large audience version of our previous work (see math.AG/0301146) in which we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of $\bar{\partial}$-coherent sheaves.…

In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which…

We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.

This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In…

In this paper, we discuss the construction of classifying spaces of fibre sequences in model categories of simplicial sheaves. One construction proceeds via Brown representability and provides a classification in the pointed model category.…

We study certain Poisson structures related to quantized enveloping algebras. In particular, we give a description of the Poisson structure of a certain manifold associated to the ring of differential operators.

For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…

In this work, we set up a theory of p-adic modular forms over Shimura curves over totally real fields which allows us to consider also non-integral weights. In particular, we define an analogue of the sheaves of k-th invariant differentials…

We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference…

Starting categorically, we give simple and precise models of equivariant classifying spaces. We need these models for work in progress in equivariant infinite loop space theory and equivariant algebraic K-theory, but the models are of…

Infinitary operations, such as products indexed by countably infinite linear orders, arise naturally in the context of fundamental groups and groupoids. Despite the fact that the usual binary operation of the fundamental group determines…

We study an analogue of the Parovicenko property in categories of compact spaces with additional structures. In particular, we present an internal characterization of this property in the class of compact median spaces.

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…

Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over Rep(H). When the bimodule categories are invertible this description can be given explicitly. We present some consequences…

We give explicit descriptions of all path connected components and isolated points of both spaces of composition operators and nonzero weighted composition operators acting from a Fock space $\mathcal{F}^p(\mathbb{C}^n)$ to another one…

We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.

In this paper we introduce a generalization of Hilbert C-modules which are pre- Finsler module namely C-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will…

We characterize the compact multiplication operators on a semi-crossed product in terms of the corresponding dynamical system. We also characterize the compact elements of this algebra and determine the ideal they generate.

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…

We show that the category of truncated spaces with finite homotopy invariants ($\pi$\=/finite spaces) has many of the features expected of an elementary \oo topos. It should be thought of as the natural higher analogue of the elementary…