Comptes Rendus
no. 1
Functional analysis
KK-theory of A-valued semi-circular systems
Presented by: Alain Connes
Emmanuel Germain1; Pierre Umber2
1 LMNO UMR 6139, Université de Caen et CNRS, France
2 ENS Lyon, France
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.

Received:
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 
@article{CRMATH_2016__354_1_87_0,
     author = {Emmanuel Germain and Pierre Umber},
     title = {KK-theory of {A-valued} semi-circular systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {87--90},
     year = {2016},
     publisher = {Elsevier},
     volume = {354},
     number = {1},
     doi = {10.1016/j.crma.2015.10.013},
     language = {en},
}
TY  - JOUR
AU  - Emmanuel Germain
AU  - Pierre Umber
TI  - KK-theory of A-valued semi-circular systems
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 87
EP  - 90
VL  - 354
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2015.10.013
LA  - en
ID  - CRMATH_2016__354_1_87_0
ER  - 
%0 Journal Article
%A Emmanuel Germain
%A Pierre Umber
%T KK-theory of A-valued semi-circular systems
%J Comptes Rendus. Mathématique
%D 2016
%P 87-90
%V 354
%N 1
%I Elsevier
%R 10.1016/j.crma.2015.10.013
%G en
%F CRMATH_2016__354_1_87_0
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

[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

Cited by Sources:

Comments - Policy