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The set of infinite upper-triangular totally positive Toeplitz matrices has a classical parametrisation proved by Edrei et al and originally conjectured by Schoenberg, that involves pairs of sequences of positive real parameters. These…

Representation Theory · Mathematics 2025-10-03 Konstanze Rietsch

To a graph $\Gamma$ one can associate a C^*-algebra $C^*(\Gamma)$ generated by isometries. Such $C^*$-algebras were studied recently by Crisp and Laca. They are a special case of the Toeplitz C^*-algebras $\mathcal{T}(G, P)$ associated to…

Operator Algebras · Mathematics 2007-11-07 Nikolay A. Ivanov

We show that a C*-algebra with topological dimension zero has the Global Glimm Property (every hereditary subalgebra contains an almost full nilpotent element) if and only if it is nowhere scattered (no hereditary subalgebra admits a…

Operator Algebras · Mathematics 2025-09-05 Ping Wong Ng , Hannes Thiel , Eduard Vilalta

We prove directly that if E is a directed graph in which every cycle has an entrance, then there exists a C*-algebra which is co-universal for Toeplitz-Cuntz-Krieger E-families. In particular, our proof does not invoke ideal-structure…

Operator Algebras · Mathematics 2010-01-13 Aidan Sims , Samuel B. G. Webster

We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and…

Operator Algebras · Mathematics 2024-12-18 Ramon Antoine , Francesc Perera , Hannes Thiel , Eduard Vilalta

We study from the point of view of rational equivalence the enveloping algebras of Lie algebras of dimension 3 whose derived Lie subalgebra is of dimension 2, over an algebraically closed base field in arbitrary characteristics.

Rings and Algebras · Mathematics 2022-11-11 Jacques Alev , François Dumas , César Lecoutre

We characterize the topological non-cancellative cones that are expressible as projective limits of finite powers of $[0,\infty]$. These are also the cones of lower semicontinuous extended-valued traces on AF C*-algebras. Our main result…

Operator Algebras · Mathematics 2020-09-22 Mark Moodie , Leonel Robert

We extend the usual theory of universal C*-algebras from generators and relations in order to allow some relations to be described using the strong operator topology. In particular, we can allow some infinite sum relations. We prove a…

Operator Algebras · Mathematics 2020-08-13 Giuliano Boava , Gilles G. de Castro

We study the class of simple C*-algebras introduced by Villadsen in his pioneering work on perforated ordered K-theory. We establish six equivalent characterisations of the proper subclass which satisfies the strong form of Elliott's…

Operator Algebras · Mathematics 2007-05-23 Andrew S. Toms , Wilhelm Winter

We show that Cuntz--Pimsner algebras associated to partial automorphisms twisted by vector bundles are classifiable in the sense of the Elliott program whenever the action is minimal and the base space is compact, infinite and has finite…

Operator Algebras · Mathematics 2025-06-23 Aaron Kettner

We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\cT[R]$. It is an extension of the ring C*-algebra $\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to…

Operator Algebras · Mathematics 2012-06-12 Joachim Cuntz , Christopher Deninger , Marcelo Laca

In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…

Operator Algebras · Mathematics 2013-03-04 Moritz Weber

We observe that a recent theorem of Sato, Toms-White-Winter and Kirchberg-Rordam also holds for certain nonunital C*-algebras. Namely, we show that an algebraically simple, separable, nuclear, nonelementary C*-algebra with strict…

Operator Algebras · Mathematics 2013-07-04 Bhishan Jacelon

Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains,…

Functional Analysis · Mathematics 2021-10-22 Domenico P. L. Castrigiano

We prove that an infinite block-Toeplitz matrix with finite diagonal support is totally nonnegative if and only if it is the weight matrix of a cylindrical network. This generalizes a well-known theorem of Brenti concerning finite totally…

Combinatorics · Mathematics 2025-02-21 Robert Angarone

To each monoid $P$ that embeds in a group we associate a universal Toeplitz C*-algebra $T_u(P)$ defined via generators and relations; $T_u(P)$ is a quotient of Li's semigroup C*-algebra $C^*(P)$ and they are isomorphic if and only if $P$…

Operator Algebras · Mathematics 2022-05-31 Marcelo Laca , Camila F. Sehnem

We answer an implicit question of Ian Hodkinson's. We show that atomic Pinters algebras may not be completely representable, however the class of completely representable Pinters algebras is elementary and finitely axiomatizable. We obtain…

K-Theory and Homology · Mathematics 2013-04-03 Tarek Sayed Ahmed

It is shown that a C*-algebra of the form C(X,U), where U is a UHF algebra, is not an inductive limit of subhomogeneous C*-algebras of topological dimension less than that of X. This is in sharp contrast to dimension-reduction phenomenon in…

Operator Algebras · Mathematics 2015-08-21 Aaron Tikuisis

We provide a classification, up to isomorphism, of four-dimensional ternary Leibniz algebras over an algebraically closed field of characteristic zero. For each non-abelian algebra in the classification, we explicitly determine its centroid…

Rings and Algebras · Mathematics 2026-02-26 Ahmed Zahari Abdou Damdji

We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in…

Logic · Mathematics 2013-06-07 Tarek Sayed Ahmed