Related papers: Length categories of infinite height

We study geometric representation theory of Lie algebroids. A new equivalence relation for integrable Lie algebroids is introduced and investigated. It is shown that two equivalent Lie algebroids have equivalent categories of infinitesimal…

This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…

The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of…

We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We…

This paper introduces the notion of extriangulated length categories, whose prototypical examples include abelian length categories and bounded derived categories of finite dimensional algebras with finite global dimension. We prove that an…

We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…

We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these varieties as well as the containments between them.

We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…

The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions,…

We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism algebra as long as they are ordinary or defined over a prime…

We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…

We prove that the finiteness of a finitely generated category of irreducible algebraic varieties over a field of characteristic zero is decidable. We also obtain a Burnside finiteness criterion for such a category, with applications to…

We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of…

In this paper we consider representations of certain combinatorial categories, including the poset $\D$ of positive integers and division, the Young lattice $\mathscr{Y}$ of partitions of finite sets, the opposite category of the orbit…

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

We will show that every element of a finitely generated abelian group is automorphically equivalent what we will define to be a {\em representative element} in a {\em repeat-free subgroup}, and for finite abelian groups we can count the…

We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.