  Some properties of the Clifford algebras Cl(3,0), Cl(1,3), Cl(1,3)(C),
Cl(4,1) and Cl(2,4) are presented, and three isomorphisms between the
Dirac-Clifford algebra C x Cl(1,3) and Cl(4,1) are exhibited, in order to
construct conformal maps and twistors, using the paravector model of spacetime.
The isomorphism between the twistor space inner product isometry group SU(2,2)
and the group Spin+(2,4) is also investigated, in the light of a suitable
isomorphism between C x Cl(1,3) and Cl(4,1). After reviewing the conformal
spacetime structure, conformal maps are described in Minkowski spacetime as the
twisted adjoint representation of Spin+(2,4), acting on paravectors. Twistors
are then presented via the paravector model of Clifford algebras and related to
conformal maps in the Clifford algebra over the Lorentzian R(4,1) spacetime. We
construct twistors in Minkowski spacetime as algebraic spinors associated with
the Dirac-Clifford algebra C x Cl(1,3) using one lower spacetime dimension than
standard Clifford algebra formulations, since for this purpose the Clifford
algebra over R(4,1) is also used to describe conformal maps, instead of R(2,4).
Our formalism sheds some new light on the use of the paravector model and
generalizations.
