Generalized Teleparallel Theory
  We construct a theory in which the gravitational interaction is described
only by torsion, but that generalizes the Teleparallel Theory still keeping the
invariance of local Lorentz transformations in one particular case. We show
that our theory falls, to a certain limit of a real parameter, in the
$f(\bar{R})$ Gravity or, to another limit of the same real parameter, in a
modified $f(T)$ Gravity, interpolating between these two theories and still can
fall on several other theories. We explicitly show the equivalence with
$f(\bar{R})$ Gravity for cases of Friedmann-Lemaitre-Robertson-Walker flat
metric for diagonal tetrads, and a metric with spherical symmetry for diagonal
and non-diagonal tetrads. We do still four applications, one in the
reconstruction of the de Sitter universe cosmological model, for obtaining a
static spherically symmetric solution type-de Sitter for a perfect fluid, for
evolution of the state parameter $\omega_{DE}$ and for the thermodynamics to
the apparent horizon.
