  We explore two variations of the Curtright-Zachos (CZ) deformation of the
Virasoro algebra. Firstly, we introduce a scaled CZ algebra that inherits the
scaling structure found in the differential operator representation of the
magnetic translation (MT) operators. We then linearly decompose the scaled CZ
generators to derive two types of Hom-Lie deformations of the W-infinity
algebra. We discuss *-bracket formulations of these algebras and their
connection to the Moyal product. We show that the *-bracket form of the scaled
CZ algebra arises from the Moyal product, while we obtain the second type of
deformed W-infinity through a coordinate transformation of the first type of
Moyal operators. From a physical point of view, we construct the Hamiltonian of
a tight binding model (TBM) using the Wyle matrix representation of the scaled
CZ algebra. We note that the integer powers of q are linked to the quantum
fluctuations that are inherent in the Moyal product.
