On compact elements in solvable Lie groups

Almost commuting elements in compact Lie groups

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...

Survey on Controllability of Invariant Systems on Solvable Lie Groups

Known and new results on controllability of right-invariant systems on solvable Lie groups are presented and discussed. The main ideas and technique used are outlined, illustrating examples are given. Some open questions are suggested.