Elliptic involutive structures on compact Lie groups

Probability on Compact Lie Groups

Elliptic Involutive Structures and Generalized Higgs Algebroids

ELLIPTIC INVOLUTIVE STRUCTURES AND GENERALIZED HIGGS ALGEBROIDS Eric O. Korman Jonathan Block We study the module theory of two types of Lie algebroids: elliptic involutive structures (EIS) (which are equivalent to transversely holomorphic foliations) and what we call twisted generalized Higgs algebroids (TGHA). Generalizing the wellknown results in the extremal cases of flat vector bundles and...

Einstein structures on four-dimensional nutral Lie groups

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

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...