Related papers: On a generalized Fra\"iss\'e limit construction
In this paper we define a function $L$ which will allow us to (separately or simultaneously) generalize many theorems from Number Theory obtained by Wilson, Fermat, Euler, Gauss, Lagrange, Leibniz, Moser, and Sierpinski.
We provide a complete classification of the class of unital graph $C^*$-algebras - prominently containing the full family of Cuntz-Krieger algebras - showing that Morita equivalence in this case is determined by ordered, filtered…
We use Fra\" iss\'e theoretic methods to construct several universal and ultrahomogeneous Polish metric structures. Namely, universal and ultrahomogeneous Polish metric space equipped with countably many closed subsets of its powers,…
We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in $\br^d$, and the ``IFS'' refers to…
We present a purely category-theoretic characterization of retracts of Fra\"iss\'e limits. For this aim, we consider a natural version of injectivity with respect to a pair of categories (a category and its subcategory). It turns out that…
We show that finitely generated subhomogeneous C*-algebras have finite decomposition rank. As a consequence, any separable ASH C*-algebra can be written as an inductive limit of subhomogeneous C*-algebras each of which has finite…
Revised: just some typos, reorganized a bit the article. It will be published in the VIASM Annual meeting, Hanoi. We give a detailed account of Deligne's letter to Drinfeld dated June 18, 2011, in which he shows that there are finitely many…
For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite II$_1$ factors of density character $\kappa$. These estimates are maximal…
We develop the theory of Fra\"iss\'e limits for classes of finite-dimensional multi-seminormed spaces, which are defined to be vector spaces equipped with a finite sequence of seminorms. We define a notion of a Fra\"iss\'e Fr\'echet space…
Defining distances over finite fields formally by $||x-y||:=(x_1-y_1)^2+\cdots + (x_d-y_d)^2$ for $x,y\in \mathbb{F}_q^d$, distance problems naturally arise in analogy to those studied by Erd\H{o}s and Falconer in Euclidean space. Given a…
We introduce the universal unitarily graded A-algebra for a commutative ring A and an arbitrary abelian extension U of the group of units of A, and use this concept to give simplified proofs of the main theorems of co-Galois theory in the…
In this paper the concept of unbounded Fredholm operators on Hilbert C*- modules over an arbitrary C*-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert C*-modules over…
Let $S \subset \Bbb R^n$ be a smooth compact hypersurface with a strictly positive second fundamental form, $E$ be the Fourier extension operator on $S$, and $X$ be a Lebesgue measurable subset of $\Bbb R^n$. If $X$ contains a ball of each…
Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on…
We construct and study fields F with the property that F has infinitely many extensions of some fixed degree, but E*/(E*)^n is finite for every finite extension E of F and every n>0.
We obtain a characterization of the unital C*-algebras with the property that every element is a limit of products of positive elements, thereby answering a question of Murphy and Phillips.
New deformed affine algebras A_{\hbar,\eta}(\hat{g}) are defined for any simply-laced classical Lie algebra g, which are generalizations of the algebra A_{\hbar,\eta}(\hat{sl_2}) recently proposed by Khoroshkin, Lebedev and Pakuliak (KLP).…
It is now well known that a simple graph $C^*$-algebra $C^*(E)$ of a directed graph $E$ is either AF or purely infinite. In this paper, we address the question of whether this is the case for labeled graph $C^*$-algebras recently introduced…
We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive…
The paper sheds a new light on the fundamental theorems of complex analysis due to P. Fatou, F. and M. Riesz, N. N. Lusin, I. I. Privalov, and A. Beurling. Only classical tools available at the times of Fatou are used. The proofs are very…