qualitative level) to all the sectors.

Further simplification comes from the fact, that the considered system does not admit parity violating interactions. In consequence the triad orientation reflection $v\mapsto -v$ being the large symmetry provides another natural division onto superselection sectors, namely the spaces of symmetric and antisymmetric states. For the selected sector $\varepsilon=0$ this particular choice allows to further restrict the support of the functions to $\lat^+_{0} := \lat^+_{0} \cap \re^+$.

Flat Bianchi I universe {#sec:frame-B1}
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The first step in the generalization of the model presented in previous Section is an extension to the flat Bianchi I model, describing the universe with the same matter content and topology, which however while being still homogeneous is not necessarily isotropic. Its (preliminary) analysis within LQC has been initiated in [@boj-b1]. Later more detailed analysis of its kinematics and dynamics was performed in [@chiou-b1] and [@szulc-b1] (see also [@b1-mmp; @b1-evo] for a vacuum case), although the quantization prescription used there is not applicable to the noncompact cases [@cs-b1]. The first description valid also in noncompact situation was constructed in [@awe], which we will follow in this article. In this section we briefly introduce those elements of the framework, which are needed 