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A relational structure is (connected-)homogeneous if every isomorphism between finite (connected) substructures extends to an automorphism of the structure. We investigate notions which generalise (connected-)homogeneity, where…

Combinatorics · Mathematics 2012-07-19 Deborah Lockett

Let $n$ be a natural number. Recall that a C*-algebra is said to be $n$-subhomogeneous if all its irreducible representations have dimension at most $n$. In this short note, we give various approximation properties characterising…

Operator Algebras · Mathematics 2019-09-11 Tatiana Shulman , Otgonbayar Uuye

A constructive characterization of the class of uniformly $4$-connected graphs is presented. The characterization is based on the application of graph operations to appropriate vertex and edge sets in uniformly $4$-connected graphs, that…

Combinatorics · Mathematics 2025-07-11 Xiang Chen , Shuai Kou , Chengfu Qin , Liqiong Xu , Weihua Yang

I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss…

Combinatorics · Mathematics 2013-06-25 Tanya Khovanova

For any countable graph $E$, we investigate the relationship between the Leavitt path algebra $L_{\C}(E)$ and the graph C*-algebra $C^*(E)$. For graphs $E$ and $F$, we examine ring homomorphisms, ring *-homomorphisms, algebra homomorphisms,…

Operator Algebras · Mathematics 2009-12-08 Gene Abrams , Mark Tomforde

A commutative algebra is exact if its multiplication endomorphisms are trace-free and is Killing metrized if its Killing type trace-form is nondegenerate and invariant. A Killing metrized exact commutative algebra is necessarily neither…

Rings and Algebras · Mathematics 2020-05-15 Daniel J. F. Fox

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…

Logic · Mathematics 2023-04-17 Alec Fox

We investigate conditions on a graph $C^*$-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth $(1,\infty)$-summable semfinite…

Functional Analysis · Mathematics 2007-05-23 David Pask , Adam Rennie

By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal…

Operator Algebras · Mathematics 2009-03-13 Toke Meier Carlsen

We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we give necessary and sufficient conditions for a…

Operator Algebras · Mathematics 2018-06-14 Carla Farsi , Elizabeth Gillaspy , Palle Jorgensen , Sooran Kang , Judith Packer

In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology of compact Lie group C*-algebras, define Chern characters between them and show that the Chern characters in both topological and…

K-Theory and Homology · Mathematics 2014-06-09 Do Ngoc Diep , Aderemi O. Kuku , Nguyen Quoc Tho

We classify spectrum-preserving endomorphisms of stable continuous-trace C^*-algebras up to inner automorphism by a surjective multiplicative invariant taking values in finite dimensional vector bundles over the spectrum. Specializing to…

Operator Algebras · Mathematics 2007-05-23 Ilan Hirshberg

The aim of this note is to show that the automorphism and isometry groups of the C*-algebra $\l_\infty(N,B(H))$ of all bounded sequences in $B(H)$ are topologically reflexive which, as one of our former results shows, is not the case with…

Functional Analysis · Mathematics 2008-02-03 Lajos Molnar

Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes…

Quantum Physics · Physics 2023-12-18 Arthur J. Parzygnat , Benjamin P. Russo

The generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative…

Operator Algebras · Mathematics 2009-02-12 M. C. Gregg

A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to…

Operator Algebras · Mathematics 2007-05-23 Jack Spielberg

We show that it is consistent with ZFC that there is a simple nuclear non-separable C*-algebra which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the…

Operator Algebras · Mathematics 2022-06-08 Ilijas Farah , Ilan Hirshberg

The purpose of this paper is to give a systematic study of two new classes of commutative nonassociative algebras, the so-called isospectral and medial algebras. An isospectral algebra $\mathbb{A}$ is a generic commutative nonassociative…

Rings and Algebras · Mathematics 2022-10-18 Yakov Krasnov , Vladimir Tkachev

We describe a proof of the following folklore theorem: If $\cX = G/K$ is the homogeneous space of a simply connected compact semisimple Lie group with Poisson-Lie stabilizers, then the $q$-deformed algebras of regular functions $\CC[\cX_q]$…

Quantum Algebra · Mathematics 2024-09-11 Robert Yuncken

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

Operator Algebras · Mathematics 2016-10-28 Tathagata Banerjee , Ralf Meyer