Comptes Rendus
Functional analysis
KK-theory of A-valued semi-circular systems
Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 87-90.

We compute in this article the KK-theory of A-valued semi-circular systems thanks to tools developed by Pimsner (see [1]) to study generalized Toeplitz algebras.

On calcule dans cet article la KK-théorie de systèmes semi-circulaires A-valués à l'aide d'outils développés par Pimsner (voir [1]) pour étudier les algèbres de Toeplitz généralisées.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2015.10.013

Emmanuel Germain 1; Pierre Umber 2

1 LMNO UMR 6139, Université de Caen et CNRS, France
2 ENS Lyon, France
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Emmanuel Germain; Pierre Umber. KK-theory of A-valued semi-circular systems. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 87-90. doi : 10.1016/j.crma.2015.10.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.013/

[1] M.V. Pimsner A class of C-algebras generalizing both Cuntz–Krieger algebras and crossed products by Z, Waterloo, ON, 1995 (Fields Inst. Commun.), Volume vol. 12, American Mathematical Society, Providence, RI (1997), pp. 189-212

[2] D. Shlyakhtenko Free quasi-free states, Pac. J. Math., Volume 177 (1997), pp. 329-368

[3] D. Shlyakhtenko A-valued semicircular systems, J. Funct. Anal., Volume 166 (1999)

[4] D. Voiculescu The K-groups of the C-algebra of a semicircular family, K-Theory, Volume 7 (1993), pp. 5-7

[5] D. Voiculescu; K. Dykema; A. Nica Free Random Variables, CRM Monograph Ser., vol. 1, American Mathematical Society, Providence, RI, USA, 1992

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