Abstract
Algebraic and geometric features of the BRST operators are studied on coadjoint orbits of some infinite dimensional Lie groups. An extended form of the Maurer·Cartan equation for the BRST operator Q is derived and it is found that the equation plays a fundamental role in field theories constructed on infinite·dimensional group manifolds. ' Recently a powerful geometric approach to D=2 conformal field theories has been proposed. It is the method of coadjoint orbits of infinite-dimensional Lie groups for derivation of geometric D=2 field theory actions.l),2) Surprisingly enough, using the standard Kirillov-Kostant symplectic structure on the coadjoint orbits of the Virasoro group one naturally finds the geometric action of the Polyakov-Liouville gravity, whereas for the Kac-Moody group one obtains the Wess-Zumino-Novikov Witten (WZNW) action. This approach has been extended also to the super Virasoro and super-Kac-Moody groups.3) According to Alekseev and Shatashvili (AS),l) the symplectic structure can be written in terms of the I-form Y with values in the Lie algebra g. The I-form Y satisfies the equation l )
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