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Galois extensions, positive involutions and an application to unitary space-time coding (1809.08954v2)
Published 24 Sep 2018 in math.RA, cs.IT, and math.IT
Abstract: We show that under certain conditions every maximal symmetric subfield of a central division algebra with positive unitary involution $(B,\tau)$ will be a Galois extension of the fixed field of $\tau$ and will "real split" $(B,\tau)$. As an application we show that a sufficient condition for the existence of positive involutions on certain crossed product division algebras, considered by Berhuy in the context of unitary space-time coding, is also necessary, proving that Berhuy's construction is optimal.