Geometric actions and the Maurer-Cartan equation on coadjoint orbits of infinite-dimensional Lie groups

摘要

The Maurer-Cartan equation for the BRST-like operator (Omega) is derived on coadjoint orbits of some infinite-dimensional Lie groups. Its form is preserved even when the algebra has a central extension. The symplectic two-form on coadjoint orbits can be expressed in terms of (Omega). By inserting solutions (Omega) of the Maurer-Cartan equation into the symplectic two-form, we obtain geometric actions for some conformal groups. (author). (ERA citation 20:014229)