Dynamics of non-archimedean Polish groups
نویسنده
چکیده
A topological group G is Polish if its topology admits a compatible separable complete metric. Such a group is non-archimedean if it has a basis at the identity that consists of open subgroups. This class of Polish groups includes the profinite groups and (Qp, +) but our main interest here will be on non-locally compact groups. In recent years there has been considerable activity in the study of the dynamics of Polish non-archimedean groups and this has led to interesting interactions between logic, finite combinatorics, group theory, topological dynamics, ergodic theory and representation theory. In this paper I will give a survey of some of the main directions in this area of research. 2010 Mathematics Subject Classification. Primary 03C15, 22F50, 54H20, 37A15.
منابع مشابه
Spatial and Non-spatial Actions of Polish Groups
For locally compact groups all actions on a standard measure algebra have a spatial realization. For many Polish groups this is no longer the case. However, we show here that for non-archimedean Polish groups all measure algebra actions do have spatial realizations. In the other direction we show that an action of a Polish group is whirly (“ergodic at the identity”) if and only if it admits no ...
متن کاملGraev ultrametrics and surjectively universal non-Archimedean Polish groups
Article history: Received 9 November 2012 Received in revised form 13 February 2013 Accepted 17 February 2013 MSC: primary 03E15, 46B10 secondary 54H05, 46B99
متن کاملPositive-additive functional equations in non-Archimedean $C^*$-algebras
Hensel [K. Hensel, Deutsch. Math. Verein, {6} (1897), 83-88.] discovered the $p$-adic number as a number theoretical analogue of power series in complex analysis. Fix a prime number $p$. for any nonzero rational number $x$, there exists a unique integer $n_x inmathbb{Z}$ such that $x = frac{a}{b}p^{n_x}$, where $a$ and $b$ are integers not divisible by $p$. Then $|x...
متن کاملSuperstability of $m$-additive maps on complete non--Archimedean spaces
The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis.
متن کاملSystem of AQC functional equations in non-Archimedean normed spaces
In 1897, Hensel introduced a normed space which does not have the Archimedean property. During the last three decades theory of non--Archimedean spaces has gained the interest of physicists for their research in particular in problems coming from quantum physics, p--adic strings and superstrings. In this paper, we prove the generalized Hyers--Ulam--Rassias stability for a ...
متن کامل