Galois extensions, positive involutions and an application to unitary space-time coding

09/24/2018

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by   Vincent Astier, et al.

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We show that under certain conditions every maximal symmetric subfield of a central division algebra with positive unitary involution (B,τ) will be a Galois extension of the fixed field of τ and will "real split" (B,τ). 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.