Finite factor representations of Higman–Thompson groups

Finite Factor Representations of Higman-Thompson groups

We prove that the only finite factor-representations of the HigmanThompson groups {Fn,r}, {Gn,r} are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that any measure-preserving ergodic action of a simple Higman-Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.

Representations of finite groups

A micro-introduction to the theory of representations of finite groups.

Representations of Finite Groups

Representations of Finite Groups

We provide a formal framework for the theory of representations of finite groups, as modules over the group ring. Along the way, we develop the general theory of groups (relying on the group add class for the basics), modules, and vector spaces, to the extent required for theory of group representations. We then provide formal proofs of several important introductory theorems in the subject, in...

Representations of finite groups

Representations of finite groups are much simpler than those of larger ones, but they offer a model for the general theory and for that reason are very valuable as an introduction to the subject. The challenge is to present the material in such a way as to give some idea of techniques that might generalize, rather than use tricks that definitely work only for finite groups. Pursuing this goal s...