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

2018/09/24 by Astier, Vincent, Unger, Thomas
#13J30 #16W10 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Primary: 12E15 #Rings and Algebras (math.RA) #Secondary: 11T71

paper · doi:10.48550/arxiv.1809.08954

Abstract

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.

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