Geodesic
The classification of real purely infinite simple C*-algebras
Documenta mathematica, Tome 16 (2011), pp. 619-655
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We classify real Kirchberg algebras using united K-theory. Precisely, let A and B be real simple separable nuclear purely infinite C*-algebras that satisfy the universal coefficient theorem such that AC​ and BC​ are also simple. In the stable case, A and B are isomorphic if and only if KCRT(A)≅KCRT(B). In the unital case, A and B are isomorphic if and only if (KCRT(A),[1A​])≅(KCRT(B),[1B​]). We also prove that the complexification of such a real C*-algebra is purely infinite, resolving a question left open from [43]. Thus the real C*-algebras classified here are exactly those real C*-algebras whose complexification falls under the classification result of Kirchberg [26] and Phillips[35]. As an application, we find all real forms of the complex Cuntz algebras On​ for 2≤n≤∞.
DOI : 10.4171/dm/345
Classification : 19K99, 46L35, 46L80
Mots-clés : classification, K-theory, real C\*-algebras 
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     author = {Jeffrey L. Boersema and P.J. Stacey and Efren Ruiz},
     title = {The classification of real purely infinite simple {C*-algebras}},
     journal = {Documenta mathematica},
     pages = {619--655},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/345},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/345/}
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Jeffrey L. Boersema; P.J. Stacey; Efren Ruiz. The classification of real purely infinite simple C*-algebras. Documenta mathematica, Tome 16 (2011), pp. 619-655. doi: 10.4171/dm/345

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