Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 035, 22 pages      arXiv:2501.07756      https://doi.org/10.3842/SIGMA.2025.035

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

Shelley Hebert a, Slawomir Klimek b, Matt McBride a and J. Wilson Peoples c
a) Department of Mathematics and Statistics, Mississippi State University, 175 President's Cir. Mississippi State, MS 39762, USA
b) Department of Mathematical Sciences, Indiana University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA
c) Department of Mathematics, Pennsylvania State University, 107 McAllister Bld., University Park, State College, PA 16802, USA

Received January 16, 2025, in final form May 06, 2025; Published online May 12, 2025

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.

Key words: crossed products by endomorphims; $K$-theory; $s$-adic integers.

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