Related papers: Length categories of infinite height

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap of a finite metric space of strict…

This is the first of a series of papers on enriched infinity categories, seeking to reduce enriched higher category theory to the higher algebra of presentable infinity categories, which is better understood and can be approached via…

This note provides examples of all possible equality and strict inequality relations between upper and lower Abelian and Cesaro limits of sequences bounded above or below.

Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…

We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.

We extend the Weil representation of infinite-dimensional symplectic group to a representation a certain category of linear relations.

We formulate and prove finite dimensional analogs for the classical Balian-Low theorem, and for a quantitative Balian-Low type theorem that, in the case of the real line, we obtained in a previous work. Moreover, we show that these results…

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…

We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.

There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and…

This paper studies abelian categories that can be decomposed into smaller abelian categories via iterated recollements - such a decomposition we call a stratification. Examples include the categories of (equivariant) perverse sheaves and…

The characteristic polynomials of abelian varieties over the finite field $\mathbb{F}_q$ with $q=p^n$ elements have a lot of arithmetic and geometric information. They have been explicitly described for abelian varieties up to dimension 4,…

We consider an homogeneous action of a finite group on a free linear category over a field in order to prove that the subcategory of invariants is still free. Moreover we show that the representation type is preserved when considering…

We show that the quotient of the continuous cluster category $\mathcal C_\pi$ modulo the additive subcategory generated by any cluster is an abelian category and we show that it is isomorphic to the category of infinite length modules over…

Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…

The extension dimensions of an Artin algebra give a reasonable way of measuring how far an algebra is from being representation-finite. In this paper we mainly study extension dimensions linked by recollements of derived module categories…

A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…

Given a minimal surface equipped with a generically finite map to an Abelian variety, we give an optimal bound on the canonical degree of a rational or an elliptic curve. As a corollary, we obtain the finiteness of rational and elliptic…