Abstract
Algebraic and geometric features of the BRST operators are studied on coadjoint orbits of some infinite dimensional Lie groups. Special attention is paid upon central extensions of groups. An extended form of the Maurer-Cartan equation for the BRST operator Ω is derived and the geometrical foundation of the BRST formalism is explored by making use of the method of extended coadjoint orbits. Some geometric actions are found as an application of our method.
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