相关论文: The $C^*$-algebra of the Cartan motion groups
Let $\M=P\times{M}$ be a variable Mautner group. We describe the $C^*$-algebra $C^*(\M)$ of $\M$ in terms of an algebra of operator fields defined over $P\times{\C^2} $.
Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of…
We study the elementary C*-algebra whose elements are the sum of a diagonal plus a compact operator. We describe the structure of the unitary group, the sets of ideals, automorhisms and projections.
We survey the model theory of operator systems and C$^*$-algebras.
Let (G,X) be a locally compact transformation group, in which G acts freely on X. We show that the associated transformation-group C^*-algebra is a Fell algebra if and only if X is a Cartan G-space.
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…
We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.
We propose to study some properties of the $C^*$-algebra naturally built out of the fundamental action that an automaton group $G$ admits on a regular rooted trees $\tree$.
We describe the C*-algebras of the Heisenberg group H_n, n\geq 1, and the thread-like Lie group G_N, N\geq 3, in terms of C*-algebras of operator fields.
In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.
We calculate the ordered K_0-group of a graph C*-algebra and mention applications of this result to AF-algebras, states on the K_0-group of a graph algebra, and tracial states of graph algebras.
Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over…
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…
We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.
We present geometric characterizations of the partial isometries, unitaries, and invertible operators in C*-algebras and von Neumann algebras.
We show that the tensor product $A\otimes B$ over $\mathbb{C}$ of two $C^* $-algebras satisfying the \textit{NCDL} conditions has again the same property. We use this result to describe the $C^* $-algebra of the Heisenberg motion groups…
We define C*-algebras on a Fock space such that the Hamiltonians of quantum field models with positive mass are affiliated to them. We describe the quotient of such algebras with respect to the ideal of compact operators and deduce…
We introduce the notion of stationary actions in the context of C*-algebras. We develop the basics of the theory, and provide applications to several ergodic theoretical and operator algebraic rigidity problems.
The purpose of this paper is construct an embedding of the C*-algebra of the Cartan motion group of a real reductive group G into the reduced C*-algebra of G itself. The embedding has a number of applications: we shall use it to…