Related papers: Nilpotent group C*-algebras as compact quantum met…

We propose a definition of a "$C^*$-Eberlein" algebra, which is a weak form of a $C^*$-bialgebra with a sort of "unitary generator". Our definition is motivated to ensure that commutative examples arise exactly from semigroups of…

Let $G$ be a semi-simple real Lie group of real rank one and $\Gamma$ be a discrete subgroup in $G$ such that $\Gamma \backslash G$ has finite volume. We introduce a new group $C^*$-algebra $C^*_r(G, \Gamma)$, which provides a natural…

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…

We study the semigroup C*-algebra of a positive cone P of a weakly quasi-lattice ordered group. That is, P is a subsemigroup of a discrete group G with P\cap P^{-1}=\{e\} and such that any two elements of P with a common upper bound in P…

Let M be a compact spin manifold with a smooth action of the n-torus. Connes and Landi constructed theta-deformations M_{theta} of M, parameterized by n by n real skew-symmetric matrices theta. The M_{theta}'s together with the canonical…

A detailed study of the semigroup $C^\ast$-algebra is presented. This $C^\ast$-algebra appears as a "deformation" of the continuous functions algebra on a compact abelian group. Considering semigroup $C^\ast$-algebras in this framework we…

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…

For a locally compact group $G$ we look at the group algebras $C_0(G)$ and $C_r^*(G)$, and we let $f\in C_0(G)$ act on $L^2(G)$ by the multiplication operator $M(f)$. We show among other things that the following properties are equivalent:…

Let $K$ be a compact metric space and let $\varphi: K \to K$ be continuous. We study a C*-algebra $\mathcal{MC}_\varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_\varphi$ induced…

In this paper, the $C^*$-algebra of the seven-dimensional un-decomposable nilpotent Lie group is characterized explicitly for the first time(see \cite{chin}). Furthermore, the topology of its spectrum is described as a preparation for the…

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

We consider a coamenable compact quantum group $\mathbb{G}$ as a compact quantum metric space if its function algebra $\mathrm{C}(\mathbb{G})$ is equipped with a Lip-norm. By using a projection $P$ onto direct summands of the Peter--Weyl…

Let $\mathcal{G}$ be a locally compact \'{e}tale groupoid and $\mathscr{L}(L^2(\mathcal{G}))$ be the $C^*$-algebra of adjointable operators on the Hilbert $C^*$-module $L^2(\mathcal{G})$. In this paper, we discover a notion called…

For a closed cocompact subgroup $\Gamma$ of a locally compact group $G$, given a compact abelian subgroup $K$ of $G$ and a homomorphism $\rho:\hat{K}\to G$ satisfying certain conditions, Landstad and Raeburn constructed equivariant…

We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative…

For 0 < s < 1, let phi_s(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup {C_{phi_s} : 0 < s < 1} of composition operators acting on the Hardy space of the unit disk. We determine the joint approximate point…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

We show that a C*-algebra generated by an irreducible representation of a finitely generated virtually nilpotent group satisfies the universal coefficient theorem and has real rank 0. This combines with previous joint work with Gillaspy and…

We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C_p(X,G) of G-valued continuous functions on a…