Related papers: Classifying approximable algebras

An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all…

We introduce and discuss a definition of approximation of a topological algebraic system $A$ by finite algebraic systems of some class $\K$. For the case of a discrete algebraic system this definition is equivalent to the well-known…

The paper is a survey of some results about Weil algebras applicable in differential geometry, especially in some classification questions on bundles of generalized velocities and contact elements. Mainly, a number of claims concerning a…

We show that quasi-projective relation algebras and directed cylindric algebras are equivalent categorialy. We work out a Godels second incompleteness theorem for finite varibale fragments of first order logic. We show that distinct set…

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower…

Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…

We present a novel approach to the representation theory of finite dimensional algebras motivated by the emerging theory of graph limits. We introduce the rank spectrum of a finite dimensional algebra $R$ over a finite field. The elements…

The quasi-partition algebras were introduced by Daugherty and the first author as centralizers of the symmetric group. In this article, we give a more general definition of these algebras and give a construction of their simple modules. In…

Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of…

We present a form convergence theorem for sequences of sectorial forms and their associated semigroups in a complex Hilbert space. Roughly speaking, the approximating forms $a_n$ are all `bounded below' by the limiting form $a$, but in…

Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…

In this paper, we introduce discrete approximate circle bundles, a class of objects designed to serve as the data science analog of circle bundles from algebraic topology. We show that, under appropriate conditions, one can meaningfully and…

In recent work of the authors the notion of a derivation being approximately semi-inner arose as a tool for investigating (approximate) amenability questions for Banach algebras. Here we investigate this property in its own right, together…

Let $X$ be an analytic subset of $U\times C^n$ of pure dimension $k$ such that the projection of $X$ onto $U$ is a proper mapping, where $U$ is a Runge domain in $C^k$. We show that $X$ can be approximated by algebraic sets.

In this paper, we will define the reduced cross-sectional $C^*$-algebras of $C^*$-algebraic bundles over locally compact groups and show that if a $C^*$-algebraic bundle has the approximation property (defined similarly as in the discrete…

The article is developing homological algebra in modules over non-unital rings and algebras. The main application is the definition and study of (directed) homology of $(\infty,1)$-categories and of directed spaces, including relative…

We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…

In this note, we shall generalize the notion of a $P$-space to proximity spaces and investigate the basic properties of these proximities. We therefore define a $P_{\aleph_{1}}$-proximity to be a proximity where if $A_{n}\prec B$ for all…

In this paper, we will prove an analogue of Fujita's approximation theorem under the framework of Arakelov theory over adelic curves, which proves a conjecture of Huayi Chen and Atsushi Moriwaki.

We define the notion of an almost polynomial identity of an associative algebra $R$, and show that its existence implies the existence of an actual polynomial identity of $R$. A similar result is also obtained for Lie algebras and Jordan…