Related papers: On Scalable Monoids
The purpose of this note is to study some algebraic properties of irreducible ideals of monoids. We establish relations between irreducible, prime, and semiprime ideals. We explore some properties of irreducible ideals in local, Noetherian,…
We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.
In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces…
We give a classification of noncommutative algebraic monoid structures on normal affine varieties such that the group of invertible elements of the monoid is connected, solvable, and has a one-dimensional unipotent radical. We describe the…
In this paper, we study main properties of cone normed spaces, and prove some theorems of weighted means in cone normed spaces.
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
Answering a question of Frank Calegari, we extend some of our earlier results on dimension of fixed point spaces of elements in irreducible linear groups. We consider characteristic polynomials rather than just fixed spaces.
In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations $a^{\sigma(a)} = a$ with $\sigma(a)\ge 2$ for every generator $a$. The starting point for this description is the…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoidal structures on the category of right R-modules are…
This is a survey on rectifiability. I discuss basic properties of rectifiable sets, measures, currents and varifolds and their role in complex and harmonic analysis, potential theory, calculus of variations, PDEs and some other topics.
We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.
This is a supplement to the paper arXiv:q-bio/0701050, containing the text of correspondence sent to Nature in 1990.