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  • Online publication date: February 2018

4 - Lectures on Lie groups over local fields

[1] M., Abért, N., Nikolov and B., Szegedy, Congruence subgroup growth of arithmetic groups in positive characteristic. Duke Math. J. 117 (2003), 367–383.
[2] Y., Barnea and M., Larsen, A non-abelian free pro-p group is not linear over a local field. J. Algebra 214 (1999), 338–341.
[3] U., Baumgartner and G. A., Willis, Contraction groups and scales of automorphisms of totally disconnected locally compact groups. Israel J. Math. 142 (2004), 221–248.
[4] M., Bhattacharjee and D., MacPherson, Strange permutation representations of free groups. J. Aust. Math. Soc. 74 (2003), 267–285.
[5] N., Bourbaki, Vari'et'es diff'erentielles et analytiques. Fascicule de r'esultats. Hermann, Paris, 1967.
[6] N., Bourbaki, Lie groups and Lie algebras (Chapters 1–3). Springer-Verlag, Berlin, 1989.
[7] R., Camina and M., du Sautoy, Linearity of Zp [[t]]-perfect groups. Geom. Dedicata 107 (2004), 1–16.
[8] S. G., Dani and R., Shah, Contraction subgroups and semistable measures on p-adic Lie groups. Math. Proc. Cambridge Philos. Soc. 110 (1991), 299–306.
[9] S. G., Dani, N. A., Shah and G. A., Willis, Locally compact groups with dense orbits under Zd-actions by automorphisms. Ergodic Theory Dyn. Syst. 26 (2006), 1443–1465.
[10] J. D., Dixon, M. P. F., du Sautoy, A., Mann and D., Segal, Analytic pro-p groups. Cambridge Univ. Press, Cambridge, 1991.
[11] M., du Sautoy, A., Mann and D., Segal, New horizons in pro-p groups. Birkhäuser, Boston, 2000.
[12] H., Glöckner, Scale functions on p-adic Lie groups. Manuscr. Math. 97 (1998), 205–215.
[13] H., Glöckner, Contraction groups for tidy automorphisms of totally disconnected groups. Glasgow Math. J. 47 (2005), 329–333.
[14] H., Glöckner, Implicit functions from topological vector spaces to Banach spaces. Israel J. Math. 155 (2006), 205–252.
[15] H., Glöckner, Locally compact groups built up from p-adic Lie groups, for p in a given set of primes. J. Group Theory 9 (2006), 427–454.
[16] H., Glöckner, Contractible Lie groups over local fields. Math. Z. 260 (2008), 889–904.
[17] H., Glöckner, Invariant manifolds for analytic dynamical systems over ultrametric fields. Expo. Math. 31 (2013), 116–150.
[18] H., Glöckner, Finite order differentiability properties, fixed points and implicit functions over valued fields. Preprint, arXiv:math/0511218.
[19] H., Glöckner, Invariant manifolds for finite-dimensional non-archimedean dynamical systems. In: Advances in Non-Archimedean Analysis (ed. by H. Glöckner, A. Escassut and K. Shamseddine). Contemp. Math. 665 (2016), 73–90.
[20] H., Glöckner, Endomorphisms of Lie groups over local fields. To appear in: The 2016 MATRIX annals. Springer-Verlag, 2018.
[21] H., Glöckner and G. A., Willis, Uniscalar p-adic Lie groups. Forum Math. 13 (2001), 413–421.
[22] H., Glöckner and G. A., Willis, Classification of the simple factors appearing in composition series of totally disconnected contraction groups. J. Reine Angew. Math. 634 (2010), 141–169.
[23] W., Hazod and S., Siebert, Stable probability measures on Euclidean spaces and on locally compact groups. Kluwer, Dordrecht, 2001.
[24] E., Hewitt and K. A., Ross, Abstract harmonic analysis, Vol. I. Springer, Berlin, 1994.
[25] K. H., Hofmann and S. A., Morris, The Lie theory of connected pro-Lie groups. EMS, Zürich, 2007.
[26] M. C., Irwin, On the stable manifold theorem. Bull. London Math. Soc. 2 (1970), 196–198.
[27] N., Jacobson, Basic algebra II. W. H. Freeman and Company, New York, 1989.
[28] A., Jaikin-Zapirain, On linearity of finitely generated R-analytic groups. Math. Z. 253 (2006), 333–345.
[29] A., Jaikin-Zapirain and B., Klopsch, Analytic groups over general pro-p domains. J. London Math. Soc. 76 (2007), 365–383.
[30] W., Jaworski, On contraction groups of automorphisms of totally disconnected locally compact groups. Israel J. Math. 172 (2009), 1–8.
[31] A., Kepert and G. A., Willis, Scale functions and tree ends. J. Aust. Math. Soc. 70 (2001), 273–292.
[32] M., Lazard, Groupes analytiques p-adiques. Publ. Math. IHES 26 (1965), 5–219.
[33] A., Lubotzky and A., Shalev, On some Λ-analytic groups. Israel J. Math. 85 (1994), 307–337.
[34] G. A., Margulis, Discrete subgroups of semisimple Lie groups. Springer-Verlag, Berlin, 1991.
[35] T. W., Palmer, Banach algebras and the general theory of *-algebras, Vol. 2. Cambridge University Press, Cambridge, 2001.
[36] A., Parreau, Sous-groupes elliptiques de groupes linéaires sur un corps valué. J. Lie Theory 13 (2003), 271–278.
[37] C. R. E., Raja, On classes of p-adic Lie groups. New York J. Math. 5 (1999), 101–105.
[38] A. M., Robert, A course in p-adic analysis. Springer-Verlag, New York, 2000.
[39] W. H., Schikhof, Ultrametric calculus. Cambridge University Press, Cambridge, 1984.
[40] J.-P., Serre, Lie algebras and Lie groups. Springer-Verlag, Berlin, 1992.
[41] E., Siebert, Contractive automorphisms on locally compact groups. Math. Z. 191 (1986), 73–90.
[42] E., Siebert, Semistable convolution semigroups and the topology of contraction groups. In: Probability measures on groups IX. Proceedings of a conference held in Oberwolfach, January 17-23, 1988 (ed. by H., Heyer). Lecture Notes in Mathematics 1379, Springer-Verlag, Berlin, 1989, 325–343.
[43] J. S. P., Wang, The Mautner phenomenon for p-adic Lie groups. Math. Z. 185 (1984), 403–412.
[44] A., Weil, Basic number theory. Springer-Verlag, New York, 1967.
[45] J. C., Wells, Invariant manifolds of non-linear operators. Pacific J. Math. 62 (1976), 285–293.
[46] G. A., Willis, The structure of totally disconnected, locally compact groups. Math. Ann. 300 (1994), 341–363.
[47] G. A., Willis, Further properties of the scale function on a totally disconnected group. J. Algebra 237 (2001), 142–164.
[48] J. S., Wilson, Profinite groups. Oxford University Press, Oxford, 1998.