We classify all essential extensions of the form 0 → B → D → C(X) → 0 where B is a nonunital simple separable finite real rank zero Z-stable C*algebra with continuous scale, and where X is a finite CW complex. In fact, we prove that there is a group isomorphism Ext(C(X),B) → KK(C(X),M(B)/B).

Introduction. It has been shown in a previous paper [3]1 that every algebra A with radical R, such that A/R is separable, is a homomorphic image of a certain maximal algebra which is determined to within an isomorphism by A/R, the A/R-modu\e (two-sided) R/R1, and the index of nilpotency of R. Furthermore, some indication was given of how the structure of maximal algebras can be determined in si...

Abstract. We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C ∗-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomo...

Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can cons...

In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type ofΣ algebra, the seed algebra, which describes exactly the behavior of a process within a labeled transition system. We have shown the possibility of characterizing the bisimulation of two processes with the isomorphism of their corresponding se...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

In the case that K is a number field, this conjecture goes back almost thirty years. The Lie algebra analogue has been formulated by J. Tate [18], D. Mumford [10], and J.-P. Serre [13]. A more precise conjecture involves comparison with the singular homology group H1(A(C),Q) for a fixed embedding K ⊂ C. If G∞ denotes the associated Hodge group (cf. §4), the “Mumford-Tate” conjecture states that...

In this paper, a continuation of [24], we investigate the S3-orbifold subalgebra (Vc)⊗3, that is, consider S3-fixed point vertex tensor product three copies universal Virasoro operator algebras Vc. Our main result is construction minimal, strong set generators for any generic values c. More precisely, show algebra type (2,4,62,82,9,102,11,123). We also two prominent examples simple correspondin...

Let A be a unital separable amenable quasidiagonal simple C∗-algebra with real rank zero, stable rank one, weakly unperforated K0(A) and with a unique tracial state. We show that A must have tracial rank zero. Suppose also that A satisfies the Universal Coefficient Theorem. Then A can be classified by its (ordered) K-theory up to isomorphism. In particular, A must be a simple AH-algebra with no...