  Inspired in discussions presented lately regarding Lorentz-violating
interaction terms in \cite{13,6}, we propose here a slightly different version
for the coupling term. We will consider a modified quantum electrodynamics with
violation of Lorentz symmetry defined in a $\left( 2+1\right) $-dimensional
spacetime. We define the Lagrangian density with a Lorentz-violating
interaction, where the the spacetime dimensionality is explicitly taken into
account in its definition. The work encompasses an analysis of this model at
both zero and finite-temperature, where very interesting features are known to
occur due to the spacetime dimensionality. With that in mind we expect that the
spacetime dimensionality may provide new insights about the radiative
generation of higher-derivative terms into the action, implying in a new
Lorentz-violating electrodynamics, as well the nonminimal coupling may provide
interesting implications on the thermodynamical quantities.
