Related papers: When Aut($\cal A$) and Homeo(Prim($\cal A$)) are h…

We obtain a kind of structure theorem for the automorphism group ${\rm Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of direct product…

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…

In this paper an automorphism of a unital C*-algebra is said to be /locally inner/ if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating…

We present some problems related to the conjugacy classes of $\mathsf{Aut}(\mathbb{N}^*)$.

We establish necessary and sufficient conditions on a (not necessarily countable) graph E for the graph C*-algebra C*(E) to be primitive. Along with a known characterization of the graphs E for which C*(E) is prime, our main result provides…

For $C^*$-algebras $A_1, A_2$ the map $(I_1,I_2)\to ker(q_{I_1}\otimes q_{I_2})$ from $Id^{\prime}(A_1)\times Id^{\prime}(A_2)$ into $Id^{\prime}(A_1\otimes_{\mathrm{min}} A_2) is a homeomorphism onto its image which is dense in the range.…

Let $Homeo(\Omega)$ be the group of all homeomorphisms of a Cantor set $\Omega$. We study topological properties of $Homeo(\Omega)$ and its subsets with respect to the uniform $(\tau)$ and weak $(\tau_w)$ topologies. The classes of…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have…

Let A be a C*-algebra. It is shown that A is an AW*-algebra if, and only if, each maximal abelian self--adjoint subalgebra of A is monotone complete. An analogous result is proved for Rickart C*-algebras; a C*-algebra is a Rickart…

In this paper, first we show that $(\g,[\cdot,\cdot],\alpha)$ is a hom-Lie algebra if and only if $(\Lambda \g^*,\alpha^*,d)$ is an $(\alpha^*,\alpha^*)$-differential graded commutative algebra. Then, we revisit representations of hom-Lie…

The complex exponential function is a local homeomorphism and gives therefore rise to an 'etale groupoid and a C*-algebra. We determine this algebra, as well as the alge bra of the complex conjugate of the exponential function.

Our purpose in this article is first, following [8], to prove that if $\alpha $, $\beta $ are any points of the open unit disc $D(0;1)$ in the complex plane ${\bf C}$ and $r$, $s$ are any positive real numbers such that ${\overline{D}}(…

Consider a normal projective variety $X$, a linear algebraic subgroup $G$ of Aut($X$), and the field $K$ of $G$-invariant rational functions on $X$. We show that the subgroup of Aut($X$) that fixes $K$ pointwise is linear algebraic. If $K$…

For A a separable unital C*-algebra and M a separable McDuff II_1-factor, we show that the space Hom_w(A,M) of weak approximate unitary equivalence classes of unital *-homomorphisms A \rightarrow M may be considered as a closed, bounded,…

The paper presents a criterion for a C*-algebra to be a coefficient algebra associated with a given endomorphism

Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${\rm Aut}_{\rm Alg} (A)$ of $A$ is isomorphic to the group $U \bigl( G(a (A)^{\rm o} ) \bigl)$ of all…

We survey the results on linear local and 2-local homomorphisms and zero products preserving operators between C$^*$-algebras, and we incorporate some new precise observations and results to prove that every bounded linear 2-local…

We study nonunital $C^*$-algebras such that for any element there exists a local unit and prove that in such algebras there are no frames. This fact was previously known only for commutative algebras. Among other results, we establish some…

Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\to B$ is said to be a $^*$-homomorphism at an element $z\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$…

A C*-algebra is called primitive if it admits a faithful and irreducible *-representation. We show that if A_1 and A_2 are separable, unital, residually finite dimensional C*-algebras that are not both two dimensional, then their unital…