• Corpus ID: 244773643

# Aspects of Noncommutative Geometry of Bunce-Deddens Algebras

@inproceedings{Klimek2021AspectsON,
title={Aspects of Noncommutative Geometry of Bunce-Deddens Algebras},
author={Sławomir Klimek and Matt McBride and John Wilson Peoples},
year={2021}
}
• Published 1 December 2021
• Mathematics
The purpose of this paper is to study noncommutative geometry of Bunce-Deddens (BD) algebras [3], [4] and their natural smooth subalgebras. Our previous, related investigations of BD algebras are contained in [13] and [14] and are mostly concerned with classifications of unbounded derivations. The main objects of study in this paper are smooth subalgebras of Bunce-Deddens algebras. The smooth subalgebras are dense *-subalgebras closed under holomorphic functional calculus and complete in their…
1 Citations

### Noncommutative geometry of the quantum disk

• Mathematics
Annals of Functional Analysis
• 2022
The purpose of this paper is to study a smooth subalgebra T ∞ of the Toeplitz C-algebra, T , an object that captures a smooth structure on the quantum disk [14]. We also study the related algebra K

## References

SHOWING 1-10 OF 24 REFERENCES

### K-Theory for Operator Algebras

I. Introduction To K-Theory.- 1. Survey of topological K-theory.- 2. Overview of operator K-theory.- II. Preliminaries.- 3. Local Banach algebras and inductive limits.- 4. Idempotents and

### Unbounded derivations in Bunce–Deddens–Toeplitz algebras

• Mathematics
Journal of Mathematical Analysis and Applications
• 2019

### UNBOUNDED DERIVATIONS IN ALGEBRAS ASSOCIATED WITH MONOTHETIC GROUPS

• Mathematics
Journal of the Australian Mathematical Society
• 2020
Abstract Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product $\text{C}^{\ast }$ -algebra $C(G)\rtimes \mathbb{Z}$

### On spectral triples on crossed products arising from equicontinuous actions

• Mathematics
• 2011
The external Kasparov product is used to construct odd and even spectral triples on crossed products of $C^*$-algebras by actions of discrete groups which are equicontinuous in a natural sense. When

### Pontryagin Duality and the Structure of Locally Compact Abelian Groups

1. Introduction to topological groups 2. Subgroups and quotient groups of Rn 3. Uniform spaces and dual groups 4. Introduction to the Pontryagin-van Kampen duality theorem 5. Duality for compact and

### Algebras generated by a weighted shift

Techniques of Olin and Thomson and of Chevreau, Pearcy and Shields are used to prove the following: If T is an injective weighted shift on H with r(T)=‖T‖ then for each L ∈ (a(T), weak-*)*, there

The basics of C*-algebras Normal operators and abelian C*-algebras Approximately finite dimensional (AF) C*-algebras $K$-theory for AF C*-algebras C*-algebras of isometries Irrational rotation