Twisted Diff \(S^ 1\)-action on loop groups and representations of the Virasoro algebra (Q917104)

Let g be a finite-dimensional Lie algebra endowed with an Ad-invariant metric, G and LG the corresponding Lie group and the loop group, respectively, and \(G^ C\) the complexification of G. There is defined a modified Hamilton action of Diff \(S^ 1\) on \(LG^ C/G^ C\) by twisting the usual action by a left translation in LG. The authors show that this action is generated by a nonequivalent moment map (so that it defines a Poisson bracket realization of a central extension of \(diff_ CS^ 1)\). The Diff \(S^ 1\) generators are expressed by means of left LG translation generators (a modification of the Sugawara formula).