  We discuss the Curtright-Zachos (CZ) deformation of the Virasoro algebra and
its extentions in terms of magnetic translation (MT) group in a discrete Bloch
electron system, so-called the tight binding model (TBM), as well as in its
continuous system. We verify that the CZ generators are essentially composed of
a specific combination of MT operators representing deformed and undeformed
$U(1)$ translational groups, which determine phase factors for a $\ast$-bracket
commutator. The phase factors can be formulated as a $\ast$-ordered product of
the commutable $U(1)$ operators by interpreting the AB phase factor of discrete
MT action as fluctuation parameter $q$ of a quantum plane. We also show that
some sequences of TBM Hamiltonians are described by the CZ generators.
