  In this paper we address the meaning of states in loop quantum cosmology
(LQC), in the context of loop quantum gravity. First, we introduce a rigorous
formulation of an embedding proposed by Bojowald and Kastrup, of LQC states
into loop quantum gravity. Then, using certain holomorphic representations, a
new class of embeddings, called b-embeddings, are constructed, following the
ideas of [1]. We exhibit a class of operators preserving each of these
embeddings, and show their consistency with the LQC quantization. In the
b-embedding case, the classical analogues of these operators separate points in
phase space. Embedding at the gauge and diffeomorphism invariant level is
discussed briefly in the conclusions.
