Solutions to central embedding problems are constructible (Q1815014)

Obstructions of the solvability of central \(\mathbb{Z}/2 \mathbb{Z}\)-embedding problems associated to orthogonal representations have been studied by Serre, Fröhlich and Crespo. For central \(\mathbb{Z}/p \mathbb{Z}\)-embedding problems associated to projective representations, there are similar results, but the hypotheses on the representations are very restrictive. In this paper, which is derived from a portion of his thesis, the author generalizes these results to give, for any central \(\mathbb{Z}/p \mathbb{Z}\)-embedding problem over a field of characteristic not \(p\), containing the \(p\)th roots of unity, a method for constructing solutions when the obstruction can be shown to be trivial via an explicit isomorphism of a matrix ring to an algebra representative of the cohomological obstruction. Four examples are provided.