Reductions of Cartan Geometry and Symmetry Breaking in Teleparallel Gravitational Gauge Theories

From considering the difference between general relativity and teleparallel gravity in relation to which part of the Lie algebra contains the values of the field strength in the formulation of gravitational gauge theories using Cartan geometry, we examine the possibilities of various different notions of reduction involving principal fibre bundles with connections admitting additional substructures in the form of Cartan geometry. The ordinary symmetry breaking in the standard model of particle physics can be regarded as a special case when the principal fibre bundles involved in the reduction admit no Cartan geometry as additional substructure. As one of the results, we obtain a framework that can accommodate the concept of symmetry breaking involving gravitational interaction that can offer a possibility for the unification of gravity and the other interactions.