A Pile of Shifts I: Crossed Products

TL;DR

This paper explores C*-algebras linked to various natural shift operations on the Hilbert space of the s-adic tree, providing insights into their algebraic structures and properties.

Contribution

It introduces and analyzes C*-algebras associated with multiple shift actions on the s-adic tree, expanding understanding of their algebraic and dynamical features.

Findings

Characterization of C*-algebras for different shift types

Identification of structural properties of these algebras

Connections between shifts and algebraic invariants

Abstract

We discuss C$^*$-algebras associated with several different natural shifts on the Hilbert space of the $s$-adic tree, that is, the tree of balls in the space of $s$-adic integers.