Compact Lie groups which act on Euclidean space without fixed points

Compact Lie Groups Which Act on Euclidean Space without Fixed Points

It is shown that a compact Lie group G with identity component Gq acts without fixed points on euclidean space if and only if G„ is nonabelian or G/G0 is not of prime power order, which completes earlier work of P. E. Conner and E. E. Floyd, Conner and D. Montgomery, and W.C. Hsiang and W.-Y. Hsiang. In this note we describe completely the class of compact Lie groups which can act without fixed...

Fixed points of analytic actions of supersoluble Lie groups on compact surfaces

We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima’s fixed point free C∞ action on S of the affine group of the line cannot be approximated by analytic actions. An example is given of an analytic, fixed point free action on S of a solvable group that is not supersoluble.

Probability on Compact Lie Groups

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.

Towards coordination algorithms on compact Lie groups

The present work considers the design of control algorithms to coordinate a swarm of identical, autonomous, cooperating agents that evolve on compact Lie groups. The objective is that the agents reach a so-called consensus state without using any external reference. In the same line of thought, a leader-follower approach where ’follower’ agents would track one ’leader’ agent is excluded, in fav...