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We recast basic topological concepts underlying differential geometry using the language and tools of noncommutative geometry. This way we characterize principal (free and proper) actions by a density condition in (multiplier) C*-algebras.…

Differential Geometry · Mathematics 2007-05-23 Paul F. Baum , Piotr M. Hajac , Rainer Matthes , Wojciech Szymanski

We show that certain pullbacks of $*$-algebras equivariant with respect to a compact group action remain pullbacks upon completing to $C^*$-algebras. This unifies a number of results in the literature on graph algebras, showing that…

Category Theory · Mathematics 2020-02-07 Alexandru Chirvasitu

We extend the theory of tensor products of C*-algebras to the larger category of Fell bundles over locally compact groups. We prove that, like in the case of C*-algebras, there exist maximal and minimal tensor products. Given two Fell…

funct-an · Mathematics 2024-12-12 Fernando Abadie

A general method of investigation of the uniqueness property for $C^*$-algebra equipped with a circle gauge action is discussed. It unifies isomorphism theorems for various crossed products and Cuntz-Krieger uniqueness theorem for…

Operator Algebras · Mathematics 2014-10-10 B. K. Kwasniewski

We study index pairings for crossed-product $C^*$-algebras arising from minimal actions on the Cantor set. We utilize Putnam's orbit-breaking AF-subalgebras and embeddings to show we can compute any index pairing for Cantor minimal system…

Operator Algebras · Mathematics 2025-06-02 Levi Lorenzo

Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\alpha) but also on the choice of an ideal…

Operator Algebras · Mathematics 2014-12-31 B. K. Kwasniewski , A. V. Lebedev

We define and systematically study nonassociative C*-algebras as C*-algebras internal to a topological tensor category. We also offer a concrete approach to these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded operators…

Quantum Algebra · Mathematics 2011-02-04 P. Bouwknegt , K. Hannabuss , V. Mathai

We associate a $C^*$-algebra to a partial action of the integers acting on the base space of a vector bundle, using the framework of Cuntz--Pimsner algebras. We investigate the structure of the fixed point algebra under the canonical gauge…

Operator Algebras · Mathematics 2025-06-23 Aaron Kettner

We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine…

Operator Algebras · Mathematics 2009-06-29 Joachim Cuntz , Xin Li

Let $R$ be a rational function. The iterations $(R^n)_n$ of $R$ gives a complex dynamical system on the Riemann sphere. We associate a $C^*$-algebra and study a relation between the $C^*$-algebra and the original complex dynamical system.…

Operator Algebras · Mathematics 2012-09-06 Tsuyoshi Kajiwara , Yasuo Watatani

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

Operator Algebras · Mathematics 2007-05-23 Ilan Hirshberg

In this paper, we will define the reduced cross-sectional $C^*$-algebras of $C^*$-algebraic bundles over locally compact groups and show that if a $C^*$-algebraic bundle has the approximation property (defined similarly as in the discrete…

Operator Algebras · Mathematics 2007-05-23 Ruy Exel , Chi-Keung Ng

The article discusses the interrelation between relative Cuntz-Pimsner algebras and partial isometric crossed products, and presents a procedure that reduces any given Hilbert bimodule to the "smallest" Hilbert bimodule yielding the same…

Operator Algebras · Mathematics 2007-05-23 B. K. Kwasniewski , A. V. Lebedev

This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

Operator Algebras · Mathematics 2015-06-01 Leonel Robert , Aaron Tikuisis

We equip the multi-pullback $C^*$-algebra $C(S^5_H)$ of a noncommutative-deformation of the 5-sphere with a free $U(1)$-action, and show that its fixed-point subalgebra is isomorphic with the $C^*$-algebra of the multi-pullback quantum…

K-Theory and Homology · Mathematics 2015-12-31 Piotr M. Hajac , Jan Rudnik

We study C*-algebra endomorphims which are special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts. We assign to such endomorphisms a geometrical invariant, representing a cohomological obstruction for them to be…

Operator Algebras · Mathematics 2011-11-21 Ezio Vasselli

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

Operator Algebras · Mathematics 2014-01-14 Terry A. Loring , Tatiana Shulman

We construct a generalized version for the free product of unital C*-algebras over a family of unital C*-subalgebras, starting from the group-analogue. When all the subalgebras are the same, we recover the free product with amalgamation…

Operator Algebras · Mathematics 2007-05-23 Stefan Teodor Bildea

We aim to characterize the category of injective *-homomorphisms between commutative C*-subalgebras of a given C*-algebra A. We reduce this problem to finding a weakly terminal commutative subalgebra of A, and solve the latter for various…

Operator Algebras · Mathematics 2016-12-02 Chris Heunen

For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A,…

Operator Algebras · Mathematics 2018-08-01 Kei Hasegawa