A Pile of Shifts II: Structure and $K$-Theory

TL;DR

This paper analyzes the structure and computes the $K$-theory groups of $C^*$-algebras associated with various shifts on the $s$-adic tree, extending previous work and providing new insights into their algebraic properties.

Contribution

It introduces a detailed analysis of $C^*$-algebras linked to different shifts on the $s$-adic tree, including their structure and $K$-theory, building upon prior research.

Findings

Describes the structure of the $C^*$-algebras

Computes the $K$-theory groups of these algebras

Extends previous analysis to new shift types

Abstract

We discuss $C^*$-algebras associated with several different natural shifts on the Hilbert space of the $s$-adic tree, continuing the analysis from [Banach J. Math. Anal. 19 (2025), 32, 30 pages, arXiv:2412.00854] and in particular we describe their structure and compute the $K$-theory groups.