A C-metric algebra consists of a unital C-algebra and a Leibniz Lip-norm on the C-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital -homomorphism from a C-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital -homomorphisms between C-metric algebras coming from -filtrations is still a Lipschitz u...

Given a finite dimensional algebra C (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension C ⋉ Ext 2 C (DC, C) of C by the CC -bimodule Ext 2 C (DC, C). We give a construction for the quiver of the relation-extension algebra in case the quiver of C has no oriented cycles. Our main result says that an algebrã C ...

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([17]) Ando-Kirchberg ([2]). In this paper we give a complete answer to their question: A C*-algebra has algebra if only satisfies Fell's condition. contrast, show that any non-trivial extension compact operators not non-abelian but even residually type I algebra. particular its...

We introduce the notion of fibred action of a group bundle on a C0(X)algebra. By using such a notion, a characterization in terms of induced C*-bundles is given for C*-dynamical systems such that the relative commutant of the fixed-point C*-algebra is minimal (i.e., it is generated by the centre of the given C*-algebra and the centre of the fixed-point C*algebra). A class of examples in the set...

In this paper, we introduce a C∗-algebra associated with a proper primitive substitution. We show that the C∗-algebra is simple and purely infinite and contains the associated CuntzKrieger algebra and the crossed product C∗-algebra of the corresponding Cantor minimal system. And we calculate the K-groups.

in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

Let HH be an algebra with a distinguished element εH∈H∗εH∈H∗ and C,DC,D two coalgebras. Based on the construction of Brzeziński’s crossed coproduct, under some suitable conditions, we introduce coassociative coalgebra C×GTHβR×DC×TGHRβ×D which is more general two-sided coproduct structure including smash coproduct. Necessary sufficient conditions for equipped tensor product C⊗H⊗DC⊗H⊗D to bialgeb...

An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.