  In this work we apply the Drinfel'd twist of Hopf algebras to the study of
deformed quantum theories. We prove that, by carefully considering the role of
the central extension, it is indeed possible to construct the universal
enveloping algebra of the Heisenberg algebra and deform it by means of a
Drinfel'd twist, which yields a noncommutative theory. Furthermore, we show
that in the second-quantization formalism the Hopf algebra structure of the
Heisenberg algebra (both undeformed and deformed) can be obtained from the Hopf
algebra of the Schrodinger fields and oscillators, as long as they are taken to
be odd generators of the osp(1|2) superalgebra. We study the deformation of the
fermionic Heisenberg algebra and present an identification with the algebra of
the one-dimensional N-extended supersymmetric quantum mechanics, possible for
even N. A second construction for the deformation of the one-dimensional
N-extended supersymmetric quantum mechanics is presented in the superspace
representation, where the supersymmetry generators are realized in terms of
operators belonging to the universal enveloping superalgebra of one bosonic and
several fermionic oscillators. In both constructions we recover, in a more
general setting, some Cliffordization results of the literature.
