Compact abelian group actions on injective factors

Lie group actions on compact

Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.

ALGEBRAIC Zd-ACTIONS ON ZERO-DIMENSIONAL COMPACT ABELIAN GROUPS

In 1967 Furstenberg proved that every infinite closed subset of T = R/Z simultaneously invariant under multiplication by 2 and by 3 is equal to T (cf. [8]), which motivated the still unresolved question whether this scarcity of invariant sets is paralleled by a corresponding scarcity of invariant probability measures: is Lebesgue measure the only nonatomic probability measure on T which is inva...

Differentiable Actions of Compact Abelian Lie Groups on S»

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

Bracket Products on Locally Compact Abelian Groups

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).