Simplicity of certain groups of diffeomorphisms

Simplicity of Certain Groups of Diffeomorphisms

D. Epstein has shown [1] that for quite general groups of homeomorphisms, the commutator subgroup is simple. In particular, let M be a manifold. (In this note, we assume all manifolds are finite dimensional, Hausdorff, class C, and have a countable basis for their topology.) By a C r + mapping (resp. diffeomorphism) we mean a C mapping (resp. diffeomorphism) whose rth derivative is Lipschitz. L...

Simplicity of the Reduced C-algebras of Certain Coxeter Groups

Let (G, S) be a finitely generated Coxeter group, such that the Coxeter system is indecomposable and the canonical bilinear form is indefinite but non-degenerate. We show that the reduced C∗-algebra of G is simple with unique normalised trace. For an arbitrary finitely generated Coxeter group we prove the validity of a Haagerup inequality: There exist constants C > 0 and Λ ∈ N such that for a f...

The Simplicity of Certain Nonassociative

Introduction. Let V be an additively written elementary £-group of order pn, where w>l, and let (u, v), yp(u, v) he two alternate biadditive functions defined on V and with values in a field K of characteristic p. Let & be a fixed nonzero element in V, and assume that the following two conditions are satisfied: (0.1) If a, P are nonzero elements in K then a<p(u, v) +P\f/(u, v)=0 lor all v im...

On Groups of Diffeomorphisms

I. We consider here the groups of homeomorphisms on Euclidean w-space and the «-sphere Sn. Chiefly we will be concerned with the question of whether or not these groups reduce in an homotopy sense to the ordinary orthogonal group acting on these spaces. Such questions are intimately connected with the theory of fibre bundles in which these spaces occur as fibres. We will restrict ourselves to t...

Groups of Circle Diffeomorphisms