On Characters of Inductive Limits of Symmetric Groups

@article{Dudko2011OnCO,
  title={On Characters of Inductive Limits of Symmetric Groups},
  author={Artem Dudko and Konstantin Medynets},
  journal={arXiv: Representation Theory},
  year={2011}
}

Figures from this paper

Characters of the group $\mathrm{EL}_d (R)$ for a commutative Noetherian ring $R$

Let $R$ be a commutative Noetherian ring with unit. We classify the characters of the group $\mathrm{EL}_d (R)$ provided that $d$ is greater than the stable range of the ring $R$. It follows that

Invariant random subgroups of lamplighter groups

Let G be one of the lamplighter groups $${({\Bbb Z}/p{\Bbb Z})^n} \wr {\Bbb Z}$$ and Sub(G) the space of all subgroups of G. We determine the perfect kernel and Cantor-Bendixson rank of Sub(G). The

Invariant random subgroups of the lamplighter group

Let $G$ be one of the lamplighter groups $({\mathbb{Z}/p\bz})^n\wr\mathbb{Z}$ and $\Sub(G)$ the space of all subgroups of $G$. We determine the perfect kernel and Cantor-Bendixson rank of $\Sub(G)$.

Finite Factor Representations of Higman-Thompson groups

We prove that the only finite factor-representations of the Higman-Thompson groups $\{F_{n,r}\}$, $ \{G_{n,r}\}$ are the regular representations and scalar representations arising from group

On rigid stabilizers and invariant random subgroups of groups of homeomorphisms

A generalization of the double commutator lemma for normal subgroups is shown for invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As an application, we

On diagonal actions of branch groups and the corresponding characters

Discrete locally finite full groups of Cantor set homeomorphisms

This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a. topological full groups). We determine that any piecewise full group that is

Self-similar groups acting essentially freely on the boundary of the binary rooted tree

We study the class of groups generated by automata that act essentially freely on the boundary of a rooted tree. In the process we establish and discuss some general tools for determining if a group

References

SHOWING 1-10 OF 54 REFERENCES

Topologies on the group of Borel automorphisms of a standard Borel space

The paper is devoted to the study of topologies on the group $\text{\rm Aut}(X,{\Cal B})$ of all Borel automorphisms of a standard Borel space $(X, {\mathcal B})$. Several topologies are introduced

Topological orbit equivalence and C*-crossed products.

The present paper has one foot within the theory of topological dynamical Systems and the other within C*-algebra theory. The link between the two is provided by Ktheory via the crossed product

Finite rank Bratteli diagrams: Structure of invariant measures

We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is shown that every

Finite and Locally Finite Groups

Preface. Introduction. Simple locally finite groups B. Hartley. Algebraic groups G.M. Seitz. Subgroups of simple algebraic groups and related finite and locally finite groups of Lie type M.W.

Automatic continuity of homomorphisms and fixed points on metric compacta

AbstractWe prove that arbitrary homomorphisms from one of the groups $$Homeo(2^\mathbb{N} ), Homeo(2^\mathbb{N} )^\mathbb{N} , Aut(\mathbb{Q}, < ), Homeo(\mathbb{R}) or Homeo(S^1 )$$ into a

Noncommutative Independence from Characters of the Infinite Symmetric Group $\mathbb{s}_\infty$

We provide an operator algebraic proof of a classical theorem of Thoma which characterizes the extremal characters of the infinite symmetric group $\mathbb{S}_\infty$. Our methods are based on

Topological properties of full groups

Abstract We study full groups of countable, measure-preserving equivalence relations. Our main results include that they are all homeomorphic to the separable Hilbert space and that every

Group Rings of Simple Locally Finite Groups

This is an expository paper which describes some new ideas and results on the group rings of simple locally finite groups. The problem of describing the two-sided ideal lattice is restated in terms

Direct limits of symmetric and alternating groups with strictly diagonal embeddings

Abstract. In this paper we investigate the locally finite groups which are direct limits of finite symmetric or alternating groups. Our main result is to complete classification of limit groups of

Characters on the full group of an ergodic hyperfinite equivalence relation

...