We give characterizations of quasitriangular operator algebras along the line Voiculescu's characterization quasidiagonal C⁎-algebras.

This paper shows how to construct classical and quantum field C*-algebras modeling a $$U(1)^n$$ -gauge theory in any dimension using novel approach lattice gauge theory, while simultaneously constructing strict deformation quantization between the respective algebras. The construction starts with maps defined on operator systems (instead of C*-algebras) associated lattices, way that commutes al...

We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem, and compute the K-groups of our algebras.

According to a result by K. B. Lee, the lattice of varieties of pseudocomplemented distributive lattices is the ui + 1 chain B_i C Bo C Bi C • ■ ■ C Bn C •■ • C Bw in which the first three varieties are formed by trivial, Boolean, and Stone algebras respectively. In the present paper it is shown that any Stone algebra is determined within Bi by its endomorphism monoid, and that there are at mos...

This paper explores the effect of various graphical constructions upon the associated graph C∗-algebras. The graphical constructions in question arise naturally in the study of flow equivalence for topological Markov chains. We prove that outsplittings give rise to isomorphic graph algebras, and in-splittings give rise to strongly Morita equivalent C∗-algebras. We generalise the notion of a del...

We show that the method to construct C∗-algebras from topological graphs, introduced in our previous paper, generalizes many known constructions. We give many ways to make new topological graphs from old ones, and study the relation of C∗-algebras constructed from them. We also give a characterization of our C∗-algebras in terms of their representation theory.

We investigate the ideal structures of the C∗-algebras arising from topological graphs. We give the complete description of ideals of such C∗-algebras which are invariant under the so-called gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C∗algebras to be simple, prime or primitive. We completely deter...

The concept of the direct product finite family \(\textit{B}\)-algebras is introduced by Lingcong and Endam [J. A. V. Lingcong, J. C. Endam, Int. Algebra, \(\textbf{10}\) (2016), 33--40]. In this paper, we introduce infinite BCC-algebras prove that it a dual (dBCC-algebras), call external dBCC-algebra induced BCC-algebras, which general in sense Endam. We find result special subsets BCC-algebra...

We introduce a notion of covering dimension for Cuntz semigroups C⁎-algebras. This is always bounded by the nuclear C⁎-algebra, and subhomogeneous C⁎-algebras both dimensions agree. Z-stable have at most one. Further, semigroup simple, C⁎-algebra zero-dimensional if only has real rank zero or stably projectionless.