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For a long time, practitioners of the art of operator algebras always worked over the complex numbers, and nobody paid much attention to real C*-algebras.
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Charles Doran, Stefan Méndez-Diez, and Jonathan Rosenberg, T-duality for orientifolds and twisted KR-theory , Lett. Math. Phys. 104
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by same author, Graded Brauer groups of a groupoid with involution , J. Funct. Anal. 266
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by same author, String theory on elliptic curve orientifolds and K R KR -theory , Comm. Math. Phys. 335
2015
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by same author, Real Baum-Connes assembly and T-duality for torus orientifolds , J. Geom. Phys. 89
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