M. Abert, N. Bergeron, I. Biringer, T. Gelander, N. Nikolov, J. Raimbault and I. Samet, On the growth of \(\operatorname{ L}^{2}\)-invariants for sequences of lattices in Lie groups, Ann. Math., 185 (2017), 711–790.
MathSciNet
MATH
Article
Google Scholar
M. Abert, Y. Glasner and B. Virag, Kesten’s theorem for invariant random subgroups, Duke Math. J., 163 (2014), 465–488.
MathSciNet
MATH
Article
Google Scholar
V. Alekseev and R. Brugger, On invariant random positive definite functions, arXiv:1804.10471.
U. Bader, R. Boutonnet, C. Houdayer and J. Peterson, Charmenability of arithmetic groups of product type, arXiv:2009.09952.
U. Bader and A. Furman, Boundaries, rigidity of representations, and Lyapunov exponents, in Proceedings of the International Congress of Mathematicians–Seoul 2014, Vol. III, pp. 71–96, Kyung Moon Sa, Seoul, 2014.
Google Scholar
U. Bader and Y. Shalom, Factor and normal subgroup theorems for lattices in products of groups, Invent. Math., 163 (2006), 415–454.
MathSciNet
MATH
Article
Google Scholar
B. Bekka, Restrictions of unitary representations to lattices and associated \(\operatorname{C}^{*}\)-algebras, J. Funct. Anal., 143 (1997), 33–41.
MathSciNet
MATH
Article
Google Scholar
B. Bekka, Operator-algebraic superridigity for \(\operatorname{SL}_{n}(\mathbf{Z})\), \(n \geq 3\), Invent. Math., 169 (2007), 401–425.
MathSciNet
MATH
Article
Google Scholar
B. Bekka, Character rigidity of simple algebraic groups, Math. Ann., 378 (2020), 1223–1243.
MathSciNet
MATH
Article
Google Scholar
B. Bekka, M. Cowling and P. de la Harpe, Some groups whose reduced \(\operatorname{C}^{*}\)-algebra is simple, Publ. Math. Inst. Hautes Études Sci., 80 (1994), 117–134.
MathSciNet
MATH
Article
Google Scholar
B. Bekka and C. Francini, Characters of algebraic groups over number fields, arXiv:2002.07497.
B. Bekka and M. Kalantar, Quasi-regular representations of discrete groups and associated \(\operatorname{C}^{*}\)-algebras, Trans. Am. Math. Soc., 373 (2020), 2105–2133.
MathSciNet
MATH
Article
Google Scholar
É. Breuillard, M. Kalantar, M. Kennedy and N. Ozawa, \(\operatorname{C}^{*}\)-simplicity and the unique trace property for discrete groups, Publ. Math. Inst. Hautes Études Sci., 126 (2017), 35–71.
MathSciNet
MATH
Article
Google Scholar
N. P. Brown and N. Ozawa, \(\operatorname{C}^{*}\)-Algebras and Finite-Dimensional Approximations, Graduate Studies in Mathematics, vol. 88, Am. Math. Soc., Providence, 2008.
MATH
Google Scholar
A. Connes and V. F. R. Jones, Property T for von Neumann algebras, Bull. Lond. Math. Soc., 17 (1985), 57–62.
MathSciNet
MATH
Article
Google Scholar
D. Creutz and J. Peterson, Stabilizers of ergodic actions of lattices and commensurators, Trans. Am. Math. Soc., 369 (2017), 4119–4166.
MathSciNet
MATH
Article
Google Scholar
D. Creutz and J. Peterson, Character rigidity for lattices and commensurators, arXiv:1311.4513.
A. Dudko and K. Medynets, Finite factor representations of Higman-Thompson groups, Groups Geom. Dyn., 8 (2014), 375–389.
MathSciNet
MATH
Article
Google Scholar
A. Furman, Random Walks on Groups and Random Transformations. Handbook of Dynamical Systems, vol. 1A, pp. 931–1014, North-Holland, Amsterdam, 2002.
MATH
Google Scholar
H. Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. Math., 77 (1963), 335–386.
MathSciNet
MATH
Article
Google Scholar
H. Furstenberg, Non commuting random products, Trans. Am. Math. Soc., 108 (1963), 377–428.
MATH
Article
Google Scholar
H. Furstenberg, Poisson boundaries and envelopes of discrete groups, Bull. Am. Math. Soc., 73 (1967), 350–356.
MathSciNet
MATH
Article
Google Scholar
H. Furstenberg, Boundary Theory and Stochastic Processes on Homogeneous Spaces, in Harmonic Analysis on Homogeneous Spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), Proc. Sympos. Pure Math., vol. XXVI, pp. 193–229, Am. Math. Soc., Providence, 1973.
Chapter
Google Scholar
L. Ge and R. Kadison, On tensor products for von Neumann algebras, Invent. Math., 123 (1996), 453–466.
MathSciNet
MATH
Article
Google Scholar
T. Gelander, A Lecture on Invariant Random Subgroups. New Directions in Locally Compact Groups, London Math. Soc. Lecture Note Ser., vol. 447, pp. 186–204, Cambridge University Press, Cambridge, 2018.
MATH
Book
Google Scholar
E. Glasner and B. Weiss, Uniformly Recurrent Subgroups. Recent Trends in Ergodic Theory and Dynamical Systems, Contemp. Math., vol. 631, pp. 63–75, Am. Math. Soc., Providence, 2015.
MATH
Google Scholar
I. Ya. Goldsheid and G. A. Margulis, Lyapunov indices of a product of random matrices, Russ. Math. Surv., 44 (1989), 11–71.
Article
Google Scholar
U. Haagerup, A new look at \(\operatorname{C}^{*}\)-simplicity and the unique trace property of a group, in Operator Algebras and Applications–the Abel Symposium 2015, Abel Symp., vol. 12, pp. 167–176, Springer, Berlin, 2017.
Google Scholar
Y. Hartman and M. Kalantar, Stationary \(\operatorname{C}^{*}\)-dynamical systems, J. Eur. Math. Soc. (JEMS), in press. arXiv:1712.10133.
V. F. R. Jones, Ten Problems. Mathematics: Frontiers and Perspectives, pp. 79–91, Am. Math. Soc., Providence, 2000.
Google Scholar
M. Kalantar and M. Kennedy, Boundaries of reduced \(\operatorname{C}^{*}\)-algebras of discrete groups, J. Reine Angew. Math., 727 (2017), 247–267.
MathSciNet
MATH
Google Scholar
M. Kennedy, An intrinsic characterization of \(\operatorname{C}^{*}\)-simplicity, Ann. Sci. Éc. Norm. Supér., 53 (2020), 1105–1119.
MathSciNet
MATH
Article
Google Scholar
Omer Lavi and A. Levit, Characters of the group \(\operatorname{EL}_{d}(R)\) for a commutative Noetherian ring \(R\), arXiv:2007.15547.
A. Le Boudec and N. Matte Bon, Subgroup dynamics and \(\operatorname{C}^{*}\)-simplicity of groups of homeomorphisms, Ann. Sci. Éc. Norm. Supér., 51 (2018), 557–602.
MathSciNet
MATH
Article
Google Scholar
G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 17, Springer, Berlin, 1991, x+388 pp.
MATH
Book
Google Scholar
A. Nevo and R. J. Zimmer, Homogenous projective factors for actions of semi-simple Lie groups, Invent. Math., 138 (1999), 229–252.
MathSciNet
MATH
Article
Google Scholar
A. Nevo and R. J. Zimmer, A structure theorem for actions of semisimple Lie groups, Ann. Math., 156 (2002), 565–594.
MathSciNet
MATH
Article
Google Scholar
A. Nevo and R. J. Zimmer, Actions of semisimple Lie groups with stationary measure, in Rigidity in Dynamics and Geometry (Cambridge, 2000), pp. 321–343, Springer, Berlin, 2002.
MATH
Chapter
Google Scholar
N. Ozawa, A remark on fullness of some group measure space von Neumann algebras, Compos. Math., 152 (2016), 2493–2502.
MathSciNet
MATH
Article
Google Scholar
J. Peterson, Character rigidity for lattices in higher-rank groups, 2014, preprint.
J. Peterson and A. Thom, Character rigidity for special linear groups, J. Reine Angew. Math., 716 (2016), 207–228.
MathSciNet
MATH
Google Scholar
Ş. Strătilă and L. Zsidó, The commutation theorem for tensor products over von Neumann algebras, J. Funct. Anal., 165 (1999), 293–346.
MathSciNet
MATH
Article
Google Scholar
G. Stuck and R. J. Zimmer, Stabilizers for ergodic actions of higher rank semisimple groups, Ann. Math., 139 (1994), 723–747.
MathSciNet
MATH
Article
Google Scholar
M. Takesaki, Theory of operator algebras. I. Reprint of the first (1979) edition, in Operator Algebras and Non-commutative Geometry, 5, Encyclopaedia of Mathematical Sciences, vol. 124, Springer, Berlin, 2002, xx+415 pp.
Google Scholar
M. Takesaki, Theory of Operator Algebras. II, in Operator Algebras and Non-commutative Geometry, 6, Encyclopaedia of Mathematical Sciences, vol. 125, Springer, Berlin, 2003, xxii+518 pp.
Google Scholar
M. Takesaki, Theory of Operator Algebras. III, in Operator Algebras and Non-commutative Geometry, 8, Encyclopaedia of Mathematical Sciences, vol. 127, Springer, Berlin, 2003, xxii+548 pp.
Google Scholar
P. S. Wang, On isolated points in the dual spaces of locally compact groups, Math. Ann., 218 (1975), 19–34.
MathSciNet
MATH
Article
Google Scholar
R. J. Zimmer, Ergodic Theory and Semisimple Groups, Monographs in Mathematics, vol. 81, Birkhäuser, Basel, 1984, x+209 pp.
MATH
Book
Google Scholar