Geodesic
The classification of real purely infinite simple C*-algebras
Documenta mathematica, Tome 16 (2011), pp. 619-655.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $A\sc$ and $B\sc$ are also simple. In the stable case, $A$ and $B$ are isomorphic if and only if $K\crt(A) \cong K\crt(B)$. In the unital case, $A$ and $B$ are isomorphic if and only if $(K\crt(A), [1_A]) \cong (K\crt(B), [1_B])$. We also prove that the complexification of such a real C*-algebra is purely infinite, resolving a question left open from citestacey03. Thus the real C*-algebras classified here are exactly those real C*-algebras whose complexification falls under the classification result of Kirchberg citekirchberg94 and Phillips citephillips00. As an application, we find all real forms of the complex Cuntz algebras ${\O}_n$ for $2 = n leq \infty$.
Classification : 46L35, 46L80, 19K99
Keywords: real C*-algebras, $K$-theory, classification 
@article{DOCMA_2011__16__a13,
     author = {Boersema, Jeffrey L. and Ruiz, Efren and Stacey, P.J.},
     title = {The classification of real purely infinite simple {C*-algebras}},
     journal = {Documenta mathematica},
     pages = {619--655},
     publisher = {mathdoc},
     volume = {16},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a13/}
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Boersema, Jeffrey L.; Ruiz, Efren; Stacey, P.J. The classification of real purely infinite simple C*-algebras. Documenta mathematica, Tome 16 (2011), pp. 619-655. http://geodesic.mathdoc.fr/item/DOCMA_2011__16__a13/