Related papers: The Automorphism group of a simple $\mathcal{Z}$-s…

Let $A$ be a unital $C^*$-algebra. Its unitary group, $UA$, contains a wealth of topological information about $A$. However, the homotopy type of $UA$ is out of reach even for $A = M_2(\CC)$. There are two simplifications which have been…

We classify $^*$-homomorphisms from nuclear $C^*$-algebras into uniform tracial sequence algebras of nuclear $\mathcal Z$-stable $C^*$-algebras via tracial data.

We construct a simple, unital AH algebra which is shape equivalent to its tensor product with any infinite-dimensional UHF algebra, has the same tracial simplex as the said tensor product, and yet is not isomorphic to it. An analogous…

We show, based on previous results, that two separable simple stably projectionless amenable ${\cal Z}$-stable $C^*$-algebras which satisfy the UCT are isomorphic if and only if they have the same Elliott invariant.

Let $X$ be a Cantor set, and let $A$ be a unital separable simple amenable $C$*-algebra with tracial rank zero which satisfies the Universal Coefficient Theorem, we use $C(X,A)$ to denote the set of all continuous functions from $X$ to $A$,…

We prove that a graph C*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact sequence in K-theory. We prove that a similar classification also holds for a graph C*-algebra…

We study the relation between the cluster automorphisms and the quasi-automorphisms of a cluster algebra $\mathcal{A}$. We proof that under some mild condition, satisfied for example by every skew-symmetric cluster algebra, the…

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…

In the first part of the article, we consider the conjecture of K. Buzzard and T. Gee proposing that every C-algebraic automorphic representation is C-arithmetic, and we show that it can be reduced to the the analogous statement for…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an…

In this paper, we study a family of generalized Weyl algebras $\{\A\}$ and their polynomial extensions. We will show that the algebra $\A$ has a simple localization $\A_{\mathbb{S}}$ when none of $p$ and $q$ is a root of unity. As an…

We present and study C*-algebras generated by "periodic weighted creation operators" on the Fock space associated with an automorphism $\alpha$ on a C*-algebra $A$. These algebras can be viewed as generalized Bunce-Deddens algebras…

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-space is generated by a unitary…

We show that a $C^*$-algebra $\mathfrak{A}$ which is stably isomorphic to a unital graph $C^*$-algebra, is isomorphic to a graph $C^*$-algebra if and only if it admits an approximate unit of projections. As a consequence, a hereditary…

We establish axiomatic characterizations of $K$-theory and $KK$-theory for real C*-algebras. In particular, let $F$ be an abelian group-valued functor on separable real C*-algebras. We prove that if $F$ is homotopy invariant, stable, and…

In 1955 Dye proved that two von Neumann factors not of type I_2n are isomorphic (via a linear or a conjugate linear *-isomorphism) if and only if their unitary groups are isomorphic as abstract groups. We consider an analogue for…

Cuntz algebra $\mathcal O_2$ is the universal $C^*$-algebra generated by two isometries $s_1, s_2$ satisfying $s_1s_1^*+s_2s_2^*=1$. This is separable, simple, infinite $C^*$-algebra containing a copy of any nuclear $C^*$-algebra. The…

We prove that any skew-symmetrizable cluster algebra is unistructural, which is a conjecture by Assem, Schiffler, and Shramchenko. As a corollary, we obtain that a cluster automorphism of a cluster algebra $\mathcal A(\mathcal S)$ is just…

We give an example of a simple separable C*-algebra which is not isomorphic to its opposite algebra. Our example is nonnuclear and stably finite, has real rank zero and stable rank one, and has a unique tracial state. It has trivial K_1,…