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SIGMA, 2025 Volume 21, 035, 22 pp. (Mi sigma2152)

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

Shelley Heberta, Slawomir Klimekb, Matt McBridea, J. Wilson Peoplesc

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

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.

Keywords: crossed products by endomorphims, $K$-theory, $s$-adic integers.

MSC: 47L65, 46L35, 46L80

Received: January 16, 2025; in final form May 6, 2025; Published online May 12, 2025

Language: English

DOI: 10.3842/SIGMA.2025.035


ArXiv: 2501.07756


© Steklov Math. Inst. of RAS, 2025