AF-embeddability of 2-graph algebras and stable finiteness of k-graph algebras

作者: Astrid an Huef , Aidan Sims , Lisa Orloff Clark

DOI:

关键词:

摘要: We characterise stable finiteness of the C*-algebra a cofinal k-graph in terms an algebraic condition involving coordinate matrices graph. This result covers all simple C*-algebras. In special case 2-graphs we further prove that AF-embeddability, quasidiagonality and 2-graph algebra are equivalent.

参考文章(17)
M. Rørdam, F. Larsen, N. Laustsen, An Introduction to K-Theory for C*-Algebras Cambridge University Press. ,(2000) , 10.1017/CBO9780511623806
Kenneth R. Davidson, C*-algebras by example ,(1996)
D. Gwion Evans, Aidan Sims, When is the Cuntz–Krieger algebra of a higher-rank graph approximately finite-dimensional? Journal of Functional Analysis. ,vol. 263, pp. 183- 215 ,(2012) , 10.1016/J.JFA.2012.03.024
Nathanial P Brown, AF Embeddability of Crossed Products of AF Algebras by the Integers Journal of Functional Analysis. ,vol. 160, pp. 150- 175 ,(1998) , 10.1006/JFAN.1998.3339
Hiroshi Takai, On a duality for crossed products of C∗-algebras Journal of Functional Analysis. ,vol. 19, pp. 25- 39 ,(1975) , 10.1016/0022-1236(75)90004-X
Toke Meier Carlsen, Sooran Kang, Jacob Shotwell, Aidan Sims, The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆ Journal of Functional Analysis. ,vol. 266, pp. 2570- 2589 ,(2014) , 10.1016/J.JFA.2013.08.029
Lawrence Brown, Philip Green, Marc Rieffel, Stable isomorphism and strong Morita equivalence of $C^*$-algebras. Pacific Journal of Mathematics. ,vol. 71, pp. 349- 363 ,(1977) , 10.2140/PJM.1977.71.349
David Pask, Adam Rennie, Aidan Sims, The Noncommutative Geometry of k-graph C*-Algebras Journal of K-theory. ,vol. 1, pp. 259- 304 ,(2008) , 10.1017/IS007011015JKT013
David Pask, Iain Raeburn, Mikael Rørdam, Aidan Sims, Rank-two graphs whose C∗-algebras are direct limits of circle algebras Journal of Functional Analysis. ,vol. 239, pp. 137- 178 ,(2006) , 10.1016/J.JFA.2006.04.003
Lisa Orloff Clark, Jonathan Brown, Adam Sierakowski, Purely infinite $C^*$-algebras associated to \'etale groupoids arXiv: Operator Algebras. ,(2014) , 10.1017/ETDS.2014.47