Automorphism groups of right-angled buildings: Simplicity and local splittings

Fundamenta Mathematicae

Volumn 224, Issue 1, 2014, Pages 17-51

  Caprace, Pierre Emmanuel ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

BN pair; Locally compact group; Locally normal subgroup; Right angled building; Simple group

Indexed keywords

EID: 84907056579     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm224-1-2     Document Type: Article

References (22)

1. [Abe74] H. Abels, Specker-Kompaktifizierungen von lokal kompakten topologischen Gruppen, Math. Z. 135 (1973/74), 325-361.
2. [AB08] P. Abramenko and K. S. Brown, Buildings. Theory and Applications, Grad. Texts in Math. 248, Springer, New York, 2008.
3. [BEW11] Y. Barnea, M. Ershov and T. Weigel, Abstract commensurators of profinite groups, Trans. Amer. Math. Soc. 363 (2011), 5381-5417.
4. [Bou97] M. Bourdon, Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geom. Funct. Anal. 7 (1997), 245-268.
5. [CF10] P.-E. Caprace and K. Fujiwara, Rank-one isometries of buildings and quasimorphisms of Kac-Moody groups, Geom. Funct. Anal. 19 (2010), 1296-1319.
6. [CM11] P.-E. Caprace and N. Monod, Decomposing locally compact groups into simple pieces, Math. Proc. Cambridge Philos. Soc. 150 (2011), 97-128.
7. [CRW13a] P.-E. Caprace, C. Reid, and G. Willis, Locally normal subgroups of simple locally compact groups, C. R. Math. Acad. Sci. Paris 351 (2013), 657-661.
8. [CRW13b] P.-E. Caprace, C. Reid, and G. Willis, Locally normal subgroups of totally disconnected groups. Part I: General theory, arXiv: 1304.5144, 2013.
9. [CS11] P.-E. Caprace and M. Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011), 851-891.
10. [Dav98] M. W. Davis, Buildings are CAT(0), in: Geometry and Cohomology in Group Theory (Durham, 1994), London Math. Soc. Lecture Note Ser. 252, Cambridge Univ. Press, Cambridge, 1998, 108-123.
11. [Gis09] J. Gismatullin, Boundedly simple groups of automorphisms of trees, arXiv: 0905.0913 (2009).
12. [HP98] F. Haglund et F. Paulin, Simplicité de groupes d'automorphismes d'espaces à courbure négative, in: The Epstein Birthday Schrift, Geom. Topol. Monogr. 1, Geom. Topol. Publ., Coventry, 1998, 181-248.
13. [HP03] F. Haglund et F. Paulin, Constructions arborescentes d'immeubles, Math. Ann. 325 (2003), 137-164.
14. [Hée93] J.-Y. Hée, Sur la torsion de Steinberg-Ree des groupes de Chevalley et des groupes de Kac-Moody, Thèse d'État de l'Université Paris 11, Orsay, 1993.
15. [Kra09] D. Krammer, The conjugacy problem for Coxeter groups, Groups Geom. Dynam. 3 (2009), 71-171.
16. [Laz12] N. Lazarovich, Simplicity of automorphism groups of rank one cube complexes, preprint, 2012.
17. [MT09] M. Mihalik and S. Tschantz, Visual decompositions of Coxeter groups, Groups Geom. Dynam. 3 (2009), 173-198.
18. [Par07] L. Paris, Irreducible Coxeter groups, Int. J. Algebra Comput. 17 (2007), 427-447.
19. [Ron89] M. Ronan, Lectures on Buildings, Perspect. Math. 7, Academic Press, Boston, MA, 1989.
20. [Tit64] J. Tits, Algebraic and abstract simple groups, Ann. of Math. (2) 80 (1964), 313-329.
21. [Tit70] J. Tits, Sur le groupe des automorphismes d'un arbre, in: Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, 188-211.
22. [Tit74] J. Tits, Buildings of Spherical Type and Finite BN-pairs, Lecture Notes in Math. 386, Springer, Berlin, 1974.