Pell sequence and associated C^∗-algebras

In this paper, we introduce two new subclasses of Uniformly hyperfinite (briefly, UHF) algebras and Bunce–Deddens algebras, namely Pell UHF algebras and Pell Bunce–Deddens algebras, constructed via the Pell sequence. We provide a complete classification of these algebras within their respective classes. Moreover, we construct a family of AF algebras based on Pell numbers and generalized Pell numbers — referred to as Pell Approximately finite-dimensional (briefly, AF) algebras — and compute their associated K-theory invariants.