Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Boundary $ C^*$-algebras for acylindrical groups

Author(s): Guyan Robertson
Journal: Proc. Amer. Math. Soc. 136 (2008), 3851-3860.
MSC (2000): Primary 20E08, 46L80
Posted: June 3, 2008
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: Let $ \Delta$ be an infinite, locally finite tree with more than two ends. Let $ \Gamma<\operatorname{Aut}(\Delta)$ be an acylindrical uniform lattice. Then the boundary algebra $ \mathcal{A}_\Gamma = C(\partial\Delta)\rtimes \Gamma$ is a simple Cuntz-Krieger algebra whose K-theory is determined explicitly.

References:

[AD]
C. Anantharaman-Delaroche, Systèmes dynamiques non commutatifs et moyennabilité, Math. Ann. 279 (1987), 297-315. MR 919508 (89f:46127)

[BP]
A. Broise-Alamichel and F. Paulin, Sur le codage du flot géodésique dans un arbre, Annales de la Faculté des Sciences de Toulouse Math. (6) 16 (2007), 477-527. MR 2379050

[C1]
J. Cuntz, Simple $ C\sp*$-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173-185. MR 0467330 (57:7189)

[C2]
J. Cuntz, K-theory for certain $ C^*$-algebras, Ann. of Math. 113 (1981), 181-197. MR 604046 (84c:46058)

[C3]
J. Cuntz, A class of $ C^*$-algebras and topological Markov chains: Reducible chains and the Ext-functor for $ C^*$-algebras, Invent. Math. 63 (1981), 23-50. MR 608527 (82f:46073b)

[CK]
J. Cuntz and W. Krieger, A class of $ C^*$-algebras and topological Markov chains, Invent. Math. 56 (1980), 251-268. MR 561974 (82f:46073a)

[Ch]
S-S. Chen, Limit sets of automorphism groups of a tree, Proc. Amer. Math. Soc. 83 (1981), 437-441. MR 624949 (83a:05065)

[Ha]
P. de la Harpe, Topics in Geometric Group Theory, University of Chicago Press, Chicago, 2000. MR 1786869 (2001i:20081)

[K]
E. Kirchberg, Exact $ C^*$-algebras, tensor products, and the classification of purely infinite algebras, Proceedings of the International Congress of Mathematicians (Zürich, 1994), Vol. 2, 943-954, Birkhäuser, Basel, 1995. MR 1403994 (97g:46074)

[R1]
G. Robertson, Boundary actions for affine buildings and higher rank Cuntz-Krieger algebras. $ C^*$-algebras: Proceedings of the SFB Workshop on $ C^*$-algebras (Münster, March 8-12, 1999), 182-202, Springer-Verlag, 2000. MR 1798597 (2001j:46082)

[R2]
G. Robertson, Boundary operator algebras for free uniform tree lattices, Houston J. Math. 31 (2005), 913-935. MR 2148805 (2006m:46088)

[RS]
G. Robertson and T. Steger, Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras, J. Reine Angew. Math. 513 (1999), 115-144. MR 1713322 (2000j:46109)

[Sel]
Z. Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997), 527-565. MR 1465334 (98m:20045)

[Ser]
J-P. Serre, Trees, Springer-Verlag, Berlin, 1980. MR 607504 (82c:20083)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20E08, 46L80

Retrieve articles in all Journals with MSC (2000): 20E08, 46L80

Additional Information:

Guyan Robertson
Affiliation: School of Mathematics and Statistics, University of Newcastle, NE1 7RU, United Kingdom
Email: a.g.robertson@newcastle.ac.uk

DOI: 10.1090/S0002-9939-08-09453-7
PII: S 0002-9939(08)09453-7
Keywords: Acylindrical group, boundary, Cuntz-Krieger algebra
Received by editor(s): June 29, 2007,
Received by editor(s) in revised form: October 5, 2007
Posted: June 3, 2008
Communicated by: Marius Junge
Copyright of article: Copyright 2008, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google